I’ll focus on the idea of “Nazi efficiency”, since I am not as familiar with pre-Weimar Germany. The perception of this efficiency was closely tied by contemporary observers to Nazi eagerness to abandon the economic and political orthodoxies of the day – and their success in doing so in the wake of the Great Depression.

Facing a balance-of-payments crisis in 1934, for example, the Nazi government rejected the conventional approach of devaluation and instead embarked on a program of economic nationalism focused on price and import controls. As the academic journal Wirtschaftsdienst argued at the time, the choice “marked a fundamental divide between the liberal economic policies of countries such as Britain and a newly emerging system of National Socialist economic management.”

And it sort of worked! The ascent of the National Socialists inaugurated a long period of German recovery, economic expansion, and the swift end of unemployment. By 1939 the country had a labor shortage of two million people, while industrial production had more than doubled. This would have seemed amazing to countries mired in unemployment, including the US.

Of course, the Nazi recovery was far from the unqualified miracle that many contemporaries saw it to be. Generations of economic historians have since engaged in intense debates about its extent and causes, questioning whether the economic miracle was a result of “Nazi efficiency,” or an illusory artifact of fascist propaganda, and whether a similar recovery would have taken place under any regime.

And in fact the real success of Schacht’s New Plan should not be overestimated. As the historian Adam Tooze argues, for millions of Germans the economic miracle was “a highly ambiguous experience.” Its primary purpose, especially after 1935, was military rearmament rather than the welfare of ordinary Germans. [1]

But regardless of domestic sentiments, foreign audiences saw only improving trends trumpeted by Nazi propaganda. To outsiders, Germany’s emphasis on rearmament was not a liability but a signal of the regime’s ability to raise living standards while simultaneously ensuring the country’s security. In the space of only six years, it had gone from a small army and no air force to “the strongest military and air power in Europe,” writes Haffner, an achievement that “produced amazement and admiration” across Europe even as it increased anxiety among its leaders. [2]

So, whatever the empirical reality of the recovery, the “Nazi efficiency” narrative found resonance among contemporary observers for understandable reasons. The ending of unemployment “seemed to be [a] major Nazi achievement,” notes Michael Mann, and it was this perception that mattered most for spurring foreign imitation. By mid-decade “the success of the First Four-Year Plan was no longer in doubt,” wrote Guillebaud in 1939. “Recovery was no longer on paper; it was there for everybody to see.” [3,4]

Moreover, the elimination of unemployment was not just a book-keeping trick or a byproduct of propaganda. “The scale of the Nazi economic achievement should not be underestimated,” writes Ferguson; it was “real and impressive.” [5] Few observers cared whether the jobs were productive or could be linked directly to Nazi policies—what mattered was that they were created in the first place. The country’s labor service was successfully promoted “as a true symbol of National Socialism,” bolstering the regime’s prestige abroad. Goebbels had made sure that the drastic decline in unemployment would produce “astonishment and admiration throughout the Reich and far beyond Germany’s borders,” as a German newspaper put it. [6]

As Tooze concedes, “what is unarguable is that the recovery as it actually occurred bore the clear imprint of Hitler’s government.” It gave a strong impression “that a real miracle was being accomplished,” argues Haffner, “and that the man who accomplished it, Hitler, was a miracle worker.” [7,8]

EDIT: added sources and fixed a couple of typos

EDIT 2;TL/DR: just to be clear, I'm not arguing that the Nazis set the country on a path to economic stability. The ballooning debt would have been a huge problem after 1939 in the absence of a war. My only point is that the short-term successes of 1933-39, most of all the elimination of unemployment, created a credible narrative of "Nazi efficiency" in the 1930s.

Sources

1. Tooze 2006, The Wages of Destruction, p.33
2. Haffner 1978, The Meaning of Hitler, p.30
3. Michael Mann, 2004, Fascists, p.182
4. Guillebaud, C. W. 1939. The Economic Recovery of Germany: From 1933 to the Incorporation of Austria in March 1938. London: Macmillan, page 101
5. Niall Ferguson, 2006, Colossus: The Price of American Empire. p.245
6. Gotz and Patel 2006: 57, 59. “Facing the Fascist Model: Discourse and the Construction of Labour Services in the USA and Sweden in the 1930s and 1940s.” Journal of Contemporary History 41(1): 57–73.
7. Tooze 2006, p.65
8. Haffner 1978, p.27

I would like to humbly assert that there is a bit more truth to to this claim of Nazi efficiency than you are allowing for.

Nazi Germany was a leader in using state-of-the-art data management machinery. Edwin Black's excellent book IBM and the Holocaust goes into exhaustive detail over the data management capacity of the regime. From the seizure of power in the early 1930's till the surrender in 1945, the economy evolved from a minor node in the western capitalist order, to an autarkic state, and then finally to a murderous kleptocratic machine; the final two economic states would have not have been possible without the number crunching power of emerging computers.

So, to your point, I'd say part of the myth has origins in the very real increase in data management/technological capabilities, and the innovative applied uses thereof.

I'd also like to say that the reply u/Paulonium1 gives is very well written; I hope that Black's book can add some technological context as to how the actual day-to-day management and planning of the economy occurred for those interested.

As to your final point about the trope of German efficiency, I would argue that it predates Nazi Germany, however it is also only representative of one of the major strains in German thought; surely the Romantics and thinkers like Goethe would have shuddered at the thought of being considered beings whose only purpose is to efficiently execute all of their responsibilities each and every day, ad nauseam.

edit: grammar

An example of this would be the myth of German trains running on-time, so much so that you could set your watch to them. Can this be credited to the German, WWII-era government?

I know that they used trains extensively for travel and troop movement (among other things) but how could this be achieved if they were so inefficient in other aspects of governing and rule?

As an additional question, did the idea of efficiency stem from pre-war Nazi Germany? Much of the infighting and issues that I recall reading about were tied to the war effort and total war economy.

I cannot give in-depth answers, but I would like to add a basic point that has been neglected in this thread so far. Germany had a long-standing tradition of bureaucracy and effective administration, even earlier than the UK, despite the fact that it (Germany) lacked behind in modernization. Especially in Prussia a class of public officials evolved that gathered reputation not only by personal virtue, but as state personnel with accompanying professional ethics, as argued here:

Jurgen Kocka: Capitalism and Bureaucracy in German Industrialization before 1914, in: The Economic History Review New Series, Vol. 34, No. 3 (Aug., 1981), pp. 453-468.

Relevant section, p. 455:

"In 1852, in addition to some 134,000 members of the armed forces, there were about 63,000 civil servants in Prussia, or nearly 1 per cent of the labour force. Around 1910, there were 1.2 million public employees in the German Reich (including military persons), or about 4 per cent of the labour force. Rough comparison seems to show that about 1890 the proportionate importance of goverment employees in Germany was about twice as great as in Great Britain. Of course, only a small minority of these civil servants had the political power and educational background stressed above. But most of them, down to the postal employees and policemen, shared, albeit in varying degrees, important aspects of the civil service status: a specific legal status under public law, special privileges in and loyalities to the state, high esteem, and a favourable image associated with power, a sense of duty, hierarchy, formalized procedures and security. They were, so to speak, part of the state and its authority, not merely private citizens."

That topic has been reflected on in the 1930s, too:

Walter L. Dorn: The Prussian Bureaucracy in the Eighteenth Century, in: Political Science Quarterly Vol. 46, No. 3 (Sep., 1931), pp. 403-423. http://www.jstor.org/stable/2143267?seq=1#page_scan_tab_contents

EDIT: Corrected wrong number, See answers below.

In what sense are you using the word "efficient", OP? I'm surprised there hasn't been more comments asking you to qualify what you mean by that - efficient in what sense? Efficient in conduction war? Efficient in transporting materials? Efficient in use of resources? Efficient in industrial production? Efficient in mass murder?

Furthermore, what fits your definition of efficiency? What counts as efficiency? For instance: I could point out that Nazi death camps operated with massive efficiency in the murder of human beings: the use of Zyklon B vs. bullets, the cramming of victims into transport trains so that as many can be transported as possible in one car and simultaneously die of asphyxiation and other consequences during the transportation itself, etc. all worked with efficiency in mind, if "efficient" means eliminating as many people as possible as quickly and discretely as possible. These are all (literally) terribly efficient things, but you could counter that it was extremely inefficient for the Nazis to expend resources, men and desperately needed transportation/railway lines on murdering people and that's also true... So, what is "efficient"?

That all being said, I think there's a lot to be said in re: efficiency at least in terms of the Nazi War Machine. There's a lot of examples I can think of to illustrate this, but for purposes of giving an answer with sources, I'll just point out the fact that Germany entered the war with a very shaky war production footing and lacked an abundance of many necessary natural resources, the economic and industrial structure to support its own requirements, yet managed to overcome all this.

A good illustration is that - despite beginning the war more or less unable to sustain itself (in terms of capacity for sustained mass mobilization), and despite their massive loss of men, resources and the literal nonstop bombing of German cities and industry - the Nazi war machine came into peak production of armored fighting vehicles in 1944.

For a nation on the brink of collapse militarily, this is pretty remarkable. The way Germany did this can easily be called "efficiency", but can just as easily be countered as inefficient depending on how one approaches the issue. As Mark Harrison (Cambridge) points out:

The link between development level and mobilization capacity is further illustrated in the contrasting result s of German occupation in northwestern and eastern Europe. Northwestern Europe was the one high-income, industrialized region into which the Axis powers expanded. France provided Germany with as much food as all of the occupied USSR, and more industrial materials - an outcome which would have been viewed ironically from a prewar perspective, because it was the occupation of eastern Europe which was intended to make Germany self-sufficient in such deficit commodities, while the occupation of France was an accidental byproduct of the evolution of the war. (Harrison at pp. 9-10)(Emphasis added).

Harrison goes on to point out that mobilization efforts were highly successful in Germany and its economic and industrial success was highly dependent on its ability to maintain "economic integration" - AKA: "efficient" use of German economic potential in sustaining the war effort, while keeping the homefront economy intact. He notes that despite the industry being wasteful and inefficient political and administrative structure - Germany still managed to pull off maintaining their mobilization until the bitter end, basically:

In the German case, . . . it now appears that the civilian economy had become relatively highly mobilized by an early stage in the war, notwithstanding the defects of the political and administrative system. If there was slack, it was tied up in wasteful intermediate uses within military industry . . . What was important was not so much to have detailed economic controls as to be able to maintain economic integration under intense stress. This capacity is what Italy and Japan lacked." (Harrison at pp. 13)(Emphasis added)

So, what you mean by the word "efficient" is highly relative and not a monolithic yardstick we can use to measure "Germany" as a whole during 1939-45. It matters what you mean by the term "efficient", as well as the scope of your inquiry: who, what, where and when being of large consequence.

Regardless, to say the Germany was not efficient is true in many regards, but it's equally true to say Germany was certainly efficient in others, like use of economic resources for mobilization efforts, mass murder and war production as noted above.

Sources:

1. The Economics of World War II: Six Great Powers in International Comparison, pp. 1-42. Edited by Mark Harrison. Cambridge: Cambridge University Press, 1998. (Internal citations omitted)

2. Visions of Victory: The Hopes of Eight World War II Leaders, Gerhard L. Weinberd, pp. 81-111. Cambridge University Press, 2005.

I kind of miss the propaganda and ideological point in this discussion.

There was a movement in the 1920ies, combining the "old" Prussian virtues (which, by the way, are decisively calvinistic, thanks to Friedrich Wilhelm) with the "new" experiences of WWI, creating a new (German) man. This, of course, is the prototype of the new Aryan of the Nazis, who is "quick as Windhunde, hard as Kruppstahl and tough as leather".

The new man was not a fighter who enthusiastically sacrificed himself for glory and honor, as had the soldiers of 1914. Instead, driven by will, amoral, cool, functional, and hardened, he could withstand the ultimate test of battle without cracking. At the same time he was a technological warrior who understood that the war expressed the very rhythm of industrial life, as well as a man of steel who gained personal fulfillment through a narcissistic dynamism of will and energy. “All is permissible,” Gottfried Benn remarked in the late 1920s, “that leads to experience.” A certain matter-of-factness thus marked the new man, who replaced the romantic relics of a failed bourgeois age with the image of mechanical precision, a man who functioned to the rhythm of the machine. “The German factory,” despaired a French soldier in 1917, “is absorbing the world.” The Great War thus proved a breeding ground for the post-bourgeois-man, as these workers of war fashioned a true revolution.

More than any other writer, Ernst Jünger expressed and popularized this image of the new man. In the Fronterlebnis Jünger discerned the glimmerings of a new society, a world in which the worker and soldier, made one by the energy of technology and the vitalism of war, fused to create a new being who combined “a minimum of ideology with a maximum of performance,” intellectual mastery of technology with primordial soldierly qualities. War, Jünger asserted, afforded personal rebirth through passage into the intoxicating world of instinct and emotion, where men thrown together in the hurricane of battle rediscovered courage and passion.

[From "Frontsoldaten" by Stephen Fritz]

At least that is how the right wingers in the 1920ies and the Nazis afterward wanted to see themselves.