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.
Continuity mistake: In the scene where Wladyslaw Szpilman is in the parlor speaking with the German officer (just before he's about to play the piano for him), you can see his breath in the cold air every time he speaks, yet when the camera pans to the German officer, his breath isn't visible.
Chosen answer: In the scene, we see the old man being lifted in his wheelchair. Then, there is a cut-away to the family watching from across the street. Then we see someone being dumped from the chair and falling, but we never see him hit the ground. My guess from watching the scene is that the stunt person fell into a cushion which was removed in post-production. Generally, when confronted with a question such as this, I like to refer it to someone who would be in the know - in this case, the stunt team on the film. I looked up that team on IMDb.com, and searched for the individuals on Facebook. Of the twenty or so stunt people and coordinators, I could only find three with unique profiles that made me think I might have the correct individuals: Janusz Kadlubowski, Stella Kuczynska and Zbigniew Modej. I posed your question to them. However, given that I am not connected on Facebook to any of them, I have no idea if or when they would see my message and respond. I will update this answer if I receive further information.