Comedy and Nazis really works because of how Mel Brooks described it. He said (I'm paraphrasing, not quoting) that to present the Nazis as buffoons trivializes them in a way that demeans their ideology and empowers their victims. It makes it so future generations will look back at them and think, "what a bunch of dummies" and will never go down that road again.
I think there has to be a balance, though. I grew up with the impression that the Nazis were essentially just well-dressed warmongers who bumbled there way into being stupidly evil. I wasn't until I read I Cannot Forgive by Rudolf Vrba that I truly came to appreciate just how evil these guys really were. They were systematic and, dare I say, scientific in their approach to ne'er-do-welling. The Holocaust was a carefully planed strategy brewed in the mind of an evil genius (not Hitler, though fully endorsed by him). The German war-effort was largely financed and the morale of the "Arian" troops and citizenry built up by the systematic looting and destruction of (mostly but not exclusively) Jews. And the people were being told that the Jews were being deported, so most didn't know til later about the camps. They had little clue that the new shoes the Furher had provided to Fritz and Elsa's son were formerly those of a now dead Jewish boy. They just figured the Reich came through for them. This was how Germany was sustained through the rough-going war years.
While I can see how the writer's of "Patterns of Force" got it wrong, as the details were not well-known in America even by the sixties, it's difficult to see in-universe how John Gill could have gotten it so wrong. Unless "details from that period of your history are fragmentary" by the 23rd Century. The "efficiency" of the Nazi state was fueled by robbery and murder. It just doesn't work without the immoral brutality of it all, and it can't be sustained because of that brutality.
--Alex