Continuity mistake: There is a scene where the Nazis are executing some fighters after destroying their stronghold, and they line them up facing a brick wall. If you look one of them is kneeling down when they get shot, and the bullet line across the wall would not have hit her, especially as she seems to go down before she's even hit.
Continuity mistake: When Wladek Szpilman is watching the Polish uprising out his window, several rebels attack the German hospital and police station. The pavement starts out icy, but when the Germans run out of the police station, the ice has completely melted.
Continuity mistake: There are various disparities between Szpilman's hair from shot to shot. This is most noticeable when he is told to leave the first apartment; he has a centre parting which changes to being combed back when he starts to smoke the cigarette. There are also continuity problems with his beard and stubble length in some scenes.