Yet another irony... (spoilers!)
So the film determines that he is indeed the real Hitler, transported in time from the Furherbunker somehow. We can forgive the physical dissimilarities: height, eye color. But from every account I've ever read, Hitler was a dreadful bore one-on-one. He was awkward, pedantic, still, emotionless. While this Hitler was actually very charismatic with people on an individual basis, very persuasive & in his own way, sincere. No doubt the filmmakers are aware of that, but what choice did they have? Making a film, especially a comedy, featuring an actor who attempted to recreate the real Hitler's personality would have been unwatchable.
Still, I thought it an interesting decision to make him real, rather than uncover that he was some eccentric historian perhaps who finally went off the deep end.