Not a science fiction movie...

The movie doesn't show the "actual" supposed point that Hitler time traveled to the 21 century. Furthermore, I see no other element typically found in science fiction. That said, IMO, the Hitler walking around is in fact not the Hitler we all learned about from school, books, movies, documentaries, etc. This individual only believes that he is Adolf Hitler. This scenario would account for the eyes and height being incorrect, not having all the facts straight, and killing the dog.
When we see him for the first time, he's in a park laying down. He may be a vagrant, he may be mentally ill or delusional, or he may be an actor who was involved in a fight that left him unconscious and he woke up not having any memory of who he actually is. Look at the condition he's in, could his disheveled condition be because he his Adolf Hitler or more likely, could he have been involved in a fight? Suppose he is the victim of an elaborate practical joke. No one is taking this guy seriously, why should they? One thing can't be disputed, he was involved in some kind of altercation prior to us finding him in the park.
He also doesn't seem mad in the mentally ill sense. He seems rather calm, other than the scene where he passes out by the newspaper stand and the macing incident. It would be awesome to time travel, however, what if you didn't expect or anticipate it? How would you react, realizing that you've been abducted or "chosen" and were sent the future? I know there are those uber scifi people who say they'd be thrilled. How can you guess how you'd react? You can't, not until actually time traveling.
This is a mix of a what if movie as well as a point of view of society from very unusual perspective. But, in the end, the movie is funny and believable. Funny because of the bizarre antics, but believable if you feel that this is just some random individual on a bad trip or something. Remove the scifi element if you think he did time travel and you get a whole different movie.