Continuity mistake: Throughout most of the film you can see the bulge of John Cusack's supposedly missing arm through his coat.
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.