Continuity mistake: When Leo and Max first meet, Max throws water on Leo. When Leo leaves the office his shirt is magically dry.
Revealing mistake: When Max is singing the song "Betrayed", the bars of his cell shake visibly several times.
Deliberate mistake: When the police come into Max's office near the end, they force Franz Liebkind to drop his gun. Immediately after doing so, Franz cringes in pain, implying that the gun was dropped on his foot. However, the gun was dropped about 2 feet from where his foot would have been. It would have been literally impossible for the gun to have hit his foot.
Continuity mistake: Near the end of the movie, Max is yelling at Franz Liebkind in his office. Franz sits on the couch and looks very sad, about to cry. It cuts to a wider shot, and Franz is now slightly turned to the side, sobbing quite a lot. [Visible only in the widescreen version].
Other mistake: At the end of the "We Can Do It" scene, the Checker Cab the stars get into is a late model. It is definitely not the same vintage as the other 50's model cars in the movie. These cabs appear in various other street scenes.
Factual error: The Swedish girl Ulla keeps saying "God dag, min vännen" as a greeting. Problem is, the grammar is incorrect. "God dag, min vän" means "good day, my friend". "God dag, min vännen", as Ulla says, means "good day, my the friend". "Vännen" is the definite article of the Swedish word for "friend".
Continuity mistake: Before Leo and Max leave to go see Franz Liebkin and Roger DeBris, the apartment is a mess, with unread plays, pizza crust and drinks, but when they return the apartment is spotless.
Continuity mistake: In the scene where Max and Leo are trying to persuade the director to join them, his "Chrysler Building" dress changes between shots during the song. In the close up shots, one side of the collar has got caught inside the dress, then it cuts to a longer shot and it is all outside again. This happens several times during the whole routine.