Revealing mistake: During the flashback scene where Max is describing the night of the kidnapping, the rainfall at the marina is obviously fake. The "rain" is being blown at an odd angle from an off-camera fan, and the surface of the water is practically still with no raindrops. (00:40:50)
Other mistake: In a scene toward the end of the film the kidnappers argue over whether to feed the girl. One of them even says "Don't tell me to relax. You left her alone?" Later it is revealed that the two men never kidnapped anyone because it was a ruse cooked up by Max. (01:31:00)
Continuity mistake: In the last scene, Max's bathing suit changes color, from dark blue to light tan, back to dark blue.
Factual error: During the scene where Charlie's thug, Lo, is in the street with the homeless man and his "busket", Lo gets angry at him, pulls his Glock out and rakes the slide to chamber a round. However, in the next shots of Lo we see his Glock with the slide still back even though it should have returned to the closed position.
Continuity mistake: In the last scene Walken is sitting there with his hand completely untouched, no sign of any surgery or re attachment of his finger, not even a band aid.
Continuity mistake: During the last scene, Max climbs out of the water soaking wet, in the next shot he jumps down below to get the money and his shorts are completely dry.
Chosen answer: See http://www.imdb.com/title/tt0120241/soundtrack.
Myridon