Revealing mistake: Dooley Wilson (a singer, drummer, and leader of his own touring band) who played "Sam" in the film, couldn't play the piano. A pianist was playing offstage while he sang the songs. If you look at Dooley's hands whenever he is 'playing' the piano, you can see that he is not playing the proper notes.
Revealing mistake: When we see the shadow of Rick opening the safe, there is also the shadow of a candle centered in the shadow of an archway. When we see Rick closing the safe, the shadow of the candle is now at the edge of the shadow of the archway; showing that the two shots were lit differently.
Revealing mistake: Near the very beginning of the film, we see the Moroccan police car with five officers speeding through the busy street with siren blaring and people jumping out of the way. The siren continues to be heard, as the scene shifts a total of five times within eight seconds to show the panic and confusion in the streets. As the siren continues, the scene shifts back to a glimpse of the police car once again, which is going through the same section of street, with the same buildings and painted mural and the same actors on both sides of the street. Watch the man in the white suit and hat jump out of the way of the same car two times within nine seconds.