It is a bit odd that the Nazis are infamous for a list of actions that they did that are now frowned upon as people who were supportive to the ideals of fascism - genocide, militarism, censorship, hard control of human rights and so on - they also gave a lot of fascination to writers on several works of fiction and for people who write history books.
For example, one instantly recognisable feature of an archetypal Nazi is that of a Nazi officer with clean and smart uniform where you would find in many works of fiction as characters who are defined as highly disciplined.
Or another feature is their weaponry and arsenal like the many weapons that they developed in a short period of time and some of these weapons are still revered by weapons enthusiasts and experts like the MP40 sub machine gun, the STG 44 (which is technically the first fully automatic assault rifle), the Tiger and Panther tanks, the development of the largest cannon ever built, the first prototype of the first jet, the concept of Wonder Weapons and so on.
And not to mention the other things that they developed that required sophistication like the Blitzkrieg tactic and the development of certain branches in government like there was a branch that focused on propaganda, and one for the SS and so on.
These portrayals of the Nazis are ones where they were associated with efficiency and well-organised teamwork which also slightly similar to the more modern stereotypical portrayal of the German people when it comes to efficiency and effectiveness, particularly when engineering is involved.
But how accurate is this portrayal especially when compared to the drawbacks, oversight and failures that historians have found like the massive focus on propaganda during the entirety of the Nazi rule, or the waste of resources on concentration camps and the use of resources on projects that were never finished like Die Riese, or the failure of Operation Sealion and the failure of conquering the USSR and so on?
While there is some truth underpinning the perception of Nazi Germany as a peerless scientific and technological juggernaut, this pop history narrative is more myth than fact. Your question addressed a number of distinct and very broad topics- all of which are great questions- but I’ll keep my answer focused primarily on science & technology:
Germany’s continuing position as a world leader in science and technology was even stronger during the Hitler era, but this long tradition of German excellence in science & engineering far predated Hitler. While it did prove to be a major asset to his ambitions, and would have been even more so if the Nazis hadn’t chased so many highly talented Jews out of these fields, it’s important to emphasize that this tradition of excellence is a German one and has absolutely nothing to do with the National Socialists. On the contrary, scientific & technological progress actually suffered hider the NSDAP due to such policies as Deutschefisik (“German physics”) which were intended as ideologically acceptable alternatives to “Jewish” science. The many successes of German science and engineering in this era occurred in spite of Hitlerism, not because of it.
Nevertheless, the Germans of course did achieve several significant technological & scientific advancements. These are well-known and include jet engines, ballistic missiles, cryptography, and more. However, many of the most commonly cited examples were less impressive than pop history remembers them. To name a couple of examples:
The Germans also found themselves outclassed by Allied- and especially American- scientific prowess. Not only did the US easily beat Nazi Germany to the atomic bomb, but mainstays of Allied fighting power such as heavy bombers, fighter planes, the T-34 tank, semi-automatic rifles, and others were equal to and in many instances demonstrably superior to that of the Germans. The Allies also developed better radar technology and mastered its application in naval warfare far better than the Germans did, which proved the doom of the once-feared U-boat fleet. These things weren’t simply a matter of numerical superiority, either...the Allies developed a ton of highly effective tools that were simply better than Germany’s. Even some of the more better known German accomplishments weren’t that much more impressive than those of their enemies. For example, the Messerschmitt 262 is widely credited for being the world’s first combat jet fighter but the Allies’ own jet, the Gloucester Meteor, entered service at almost exactly the same time.
Did Hitler’s Germany field a plethora of fancy toys during the war? Sure, but so the Allies.
As a final note, the Germans’ famed efficiency and penchant for organizational acumen was strangely absent from many aspects of Hitler’s Germany. Procurement and production processes were notoriously inefficient and exacerbated the severe disparity in resources by making things like heavy tanks (which were already complicated and overly engineered) even slower to produce. Politically, the structure of the regime itself and its tentacles of power were bafflingly complicated. If you read about which agencies fell under which departments and department chiefs you will likely find it impossible to remember. Organizationally, there was a LOT of duplication and overlap (case in point: many officers were simultaneously members of the Gestapo and SS despite these being different organizations). This was partly by design, as Hitler enjoyed having multiple underlings scrambling to accomplish the same goal, his logic being that the “strongest” would prevail and thus the best solution would manifest itself. What resulted instead was a very inefficient, convoluted, and rivalry-ridden way of doing business. This is also the inherent weakness of a system focused on a single individual whose personal favor was the sole currency of prestige & influence, a reality that extended even to those outside the regime such as industrial leaders.