Factual error: In the famous tugboat scene, Fannie rides out on a New York Central tugboat painted jade green - a color which wasn't instituted on the boats until the early 1960s. To be accurate, the tugboat would have to have been painted red with a black stack and the New York Central logo.
Continuity mistake: During the roller skate rag number, Barbara Streisand falls and her curls in the back of her wig become loose, and when she stands up they are perfect.
Continuity mistake: At Keany's, Famny say goodbye to Nick at the backstage outside door the one with the frosted glass window), but when she leans against the door, the shot was of a quick fade in of her against the dressing room door (no window). Intentional? If so, the rapid fade in leads one to believe it was meant to be the same moment, ie. no transition.