Adolf Hitler was already a member of the German Workers' Party by the time Ernst Röhm joined it in 1919. In the movie it is depicted as the other way around.
Hitler's Niece Geli Raubal killed herself in 1931. In the movie she is murdered, 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 1934 Reichstag fire. In reality, it is still an open question as to whether it was a Nazi "false flag" operation or if they opportunistically latched onto a genuine arson to implement the Enabling Act.
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 it was being spoken at the end of the 1910s.