Deliberate mistake: When Fagin shakes Oliver's hand (when he first meets him) there is a blonde haired boy standing right behind Oliver, but in the shots from behind him, the boy is gone. This may be because the camera is just behind where the boy was and he had to move so they could get the shots from this angle.
Deliberate mistake: During "Consider Yourself", watch the meat-cutters - the cleavers they use never cut into the meat, just bounce off harmlessly. Obviously too dangerous to try and use real ones in such a crowded environment.