Adolf Hitler was already member of the German Workers' Party when Ernst Röhm joined it in 1919. In the movie it is the other way around.
Hitlers Niece Geli Raubal killed herself in 1931. In the movie she is killed, as heard by her scream, and it is suggested that Himmler killed her (since he came straight out of her room and was planning the murder in an earlier scene). Also her death in the movie happened before 1930.
Hermann Göring didn't join the party until 1923. In the movie he became a member of it in 1920. In real life Göring was in Sweden with his wife Carin in 1920.
The movie shows the Nazis planning the famous Reichstag burning. In real life it is still not clear who is actually did it until today.
Joseph Goebbels didn't visit Hitler during his arrest in Landsberg am Lech. His first meeting with him was in 1925 after his release and after "Mein Kampf" was published.
The Hitler Greeting "Sieg Heil" didn't appear in public until the mid-20s. In the movie Hitler said it already in the end 1910s.
Hitler was a faithful Christian. Therefore it is very unlikely that he would think of himself as more powerful than Jesus or that Christianity is a disease that should be fought, as shown in the movie. Even in his "Enabling Act" laws it was mentioned that christian education should be ensured.