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.
Factual error: When The Oneders are recording their song with Uncle Bob, there is an In-N-Out cup sitting by the recording equipment. There are no In-N-Out restaurants in PA.
Other mistake: Carolyn Stilton shoots Blondie O'Hara in the head and is lying dead over her dead husband. Just before the final scene starts she begins to open her eye.
Visible crew/equipment: When Jim gives his donation to Danny just after Gloria walks into the practice room for the first time, a microphone can be seen reflected in his tuba bell.