Factual error: Max and his family listen to a radio broadcast announcing the terms of the Versailles Treaty in Germany in 1919. Radio broadcasting first began in the United States in 1920 and began in Germany in 1923. Also, the radio they are listening to is a "cathedral" type that was not manufactured until the 1930s.
Continuity mistake: When Max and Hitler are talking in the restaurant and drinking lemonade, Max lights a cigarette. He blows out the smoke, and the camera angle changes. In the immediately following shot, the smoke he just exhaled isn't there anymore, and there's no implied time lapse between the lines spoken.