Factual error: When young David and his father show up at Ben Rosen's house, there is a Jewish mezuzah (a handwritten tiny scroll of parchment with a passage from the Bible enclosed in a case) affixed to the doorpost. The position of the mezuzah is incorrect. It should be higher up on the door jamb and the top should be angled towards the house, not the other way round. (00:15:00)
Continuity mistake: In the first scene where we see David Helfgott, there's a mark on his ring finger, probably made by a wedding ring. In that scene David isn't married.
Continuity mistake: At the beginning, in the cafe scene, the length of David's cigarette changes.