The Prodigal Son (1 & 2) - S2-E1
Revealing mistake: After Crockett and Tubbs' confrontation with the New York police at the end of part 1, as the police car drives away, in the background a blue car drives by and a man and woman can be seen in the car looking and pointing at the filming.
Revealing mistake: When the first scene at Emma's hideaway was shown, obviously the two characters Emma and Jessica were filmed seperately on the couch and then the film was put together (as both are played by Angela Lansbury). However Jessica did a lot of moving while she was talking, so Emma was looking straight across at where she had been, despite her bending down while she talked.
Revealing mistake: When the thief places The Blue Carbuncle in the goose's throat, it's obvious he actually doesn't put the gem in the bird's mouth. He pretends to, but then drops the gem into his other hand. This is all visible in the shot.