Responding to an post, who is now erased, but said that Goebbels was extremly talented, I would like to add that Goebbels was not only valued because he was skilled in propaganda, but also because Adolf Hitler deemed propaganda to be of the highest importance. Hitler viewed the failure of the propaganda as one of the reasons why they had lost World War I, and Mein Kampf contains a chapter solely dedicated to the question of War propaganda.
It is also important to understand the character of Goebbels disability. Goebbels had problems walking, and were not fit for war, but he could manage himself. The propaganda around those who were euthanized circled around them being an burden on society and in permanent need of assistance to be able to live. Goebbels was not handicapped in this way. Though it must be said that it surely wasn't beneficial. It is also true that there was another standard for the leaders. And at the end of the day, there were many people with more aryan characteristics than Hitler who disagreed with him, but Hitler solved this by saying that the only way he could determine if someone was an german was to announce an true german program and look who agreed to that (this was apparently said during the speech he held the 3 september at the party convention in Nürnberg, it is referenced in Ludwig von Mises' Human Action p. 76 but i haven't been able to find that particular speech.
That the Aryan archetype appeared after 1933 was unknown to me, and just scrolling through some posters I don't find anything to disprove it, but it seems weird. I don't understand why they would try to hide this, as I can't imagine it being contrary to the public opinion. Do you have any way of sourcing this?
EDIT: Goebbels were -> was (Thanks to the person who informed me of my mistake, although I can't find your post now)
I didn't know he was disabled. Without meaning to sound coarse, what were his disabilities and were the known to the general public?
Goebbels was extremely capable, loyal and dedicated to the vision of National Socialism. Unless he came into disfavor, his flaws would be 'tolerated.' Hitler tolerated vices and flaws in his subordinates, as long as they were loyal and useful to him.
Goebbels idolized Hitler, having joined the party after hearing him talk and offered his services. Hitler found that they have common ideas about peoples, men, morale and so on, so Hitler liked him. They both shared the idea that German people must be transformed through means of propaganda, culture war and total control. Goebbels offered unconditional loyalty several times and successfully pushed for propaganda - filming rallies was Goebbels idea, as well as clever usage of posters and bombastic slogans.
It should be noted that Goebbels was sent to Berlin to spread the NSDAP message. In Berlin neither Hitler nor NDSAP were popular, unlike the Communist Party or other options, so some authors think this may have been meant either as a test or as 'reassignment to Artic' since Goebbels briefly consorted with Strasser brothers (they became bitter rivals in Berlin). Goebbels managed to (eventually) make Berlin Nazi through skillful use of advertisements, speeches, street-battles and his own speeches, although urban support for Nazism was still lagging. By the time NSDAP was a power, Goebbels had proven himself.
Goebbels was also a great speaker, although not as great as Hitler since he had skill but not charisma. Goebbels managed to position himself to the place of chief propagandist and became a fixture of the Hitler regime. Organizing parades, gathering, rallies, all forms of propaganda, Goebbels became one of Hitler's most important and most trusted allies, crucial for transformation of Germany through totalitarian means. He was instrumental in organizing pogroms, caring for morale of soldiers and citizens, remaking culture and so on.
Many scholars think that Goebbels overcompensated for his disability with overachieving, so it would be hard to say that he was a drain on resources, as handicapped were thought to be. Goebbels was perhaps unfit for military service but he could certainly take care of himself. Also, his disability was result of contracting polio (not hereditary) so this was also a factor. He had six healthy children.
Sources: Longerich, P. Joseph Goebbels, Overy R., The Dictators
You won't find a specific source that explains why he was able to get away with it, but taking as a reference the books that deal with the period before the ascension of the NAZI party and the group of people that were there, we can infer a couple of things.
First Goebbles was extremely talented. And that talent was what allowed him to get into the inner circle of the party from early on, and to become the real creator of the party in the sense of public relations and propaganda. That whole mythical imagery that still surrounds the Nazi party was mostly his creation. And that takes us to our second point.
The Nazi party of the early 20's was not the same as the 30's one. They were coming from an underdog position, and they had slightly different ideals and recruitment requirements, which is evident when you realize that Hitler was not a German citizen until 1932(*). In the 1920's, and up until 1933 the party ran mainly on restoring what was lost, return to the greater days of the Reich (1871-1918 was the Second Reich), the Jews (as in the international banking clique) are to blame for everything not us, and there is no reason why we should be in such a bad situation. It is not up until after 1933, when they take power, that the whole "Aryan archetype" became a thing, and by this time most of the Party top figures were already in place, or way on their way. That's why you can see the imagery of the tall blond muscular type versus the fat Goering, or the balding Himmler, or the short club footed Goebbles.
I would recommend you to read an Kershaw's Hitler 1889-1936 Hubris, to get an in depth view of the pre-war Nazi party.
(*) The whole citizenship is complicated in this case, because he may have lost the Austrian citizenship before this date, but he didn't apply for German citizenship until 1932. The whole idea of citizenship was less ingrained that today, more taking into account that they, Austrians and Germans, belong to the same "group".
A few of the leaders of the Nazis didn't meet their parties ideal. What did the people think about that, I wonder?
Goebbels got infected with Osteomyelitis in his childhood (he was four), which lead to him developing a clubed right foot [His diaries have an entrance saying that he remembers having a long walk with his parents and for the first time having incredible pain when he was a child, maybe his clearest childhood memory]. It wasn't a genetic deficiency, it was aquired.
By the time he meets Hitler, he was a failed author, a failed journalist, a faithless socialist, poor, confused by the "chaos of the times" (his own words), a doctorate of Germanistik (German philology), working for a bank (whose soulless materialism he resented) and waiting for "a strong genius" which could renew Germany (and his life, presumably) [This fixation on geniuses has some tradition in Germany, especially in literature (think Faust)].
As we know, he met this "strong genius" in Hitler. Goebbels was immensely talented and hard working. Sometimes, however, when Goebbels felt himself rejected, he gets rather envious. His diaries, when Hitler didn't do as much as Goebbels liked about the Strasser brothers, are rather vitriolic. Another time when Goebbels swears to stop working for Hitler is when he is dissapointed that the "morphine addict", "the fat pig" Göring is made Prime Minister of Prussia instead of Goebbels.
In a way, the disability of Goebbels wasn't so bad for the Nazis. He certainly could do his share of the work (as oppossed to the Erbkranken or Geisteskranken of the Nazi pamphlets) and there was no chance that he would spread his "corruption" through his offspring. Goebbels' children and Magda (Quandt) famously were the ideal picture of all a German family should be, at least in his propaganda.
This doesn't save Goebbels from ridicule, however. Some of his enemies have called him rather pointedly nachgedunkelter Schrumpfgermane (= darkened shrink german) or Humpelstilzchen (= limp -elstilzchen, after Rumpelstiltskin, which is called Rumpelstizchen in German).