Continuity mistake: In the first scene with De Niro's first wife as Pesci arrives, he is improvising as he argues with her and he says "you call those carrots" and she says "you ate them didn't you". He replies "I got no choice". But he had flipped over the table in the prior scene as she was serving the carrots so he never even tasted them.
Continuity mistake: Early in the film there is a scene, clearly an improvisation, where De Niro's character is courting his future wife. They are sitting across from each other at a small dining table in an apartment. Apparently the director has told De Niro nothing more than "try to get her to sit on your lap", which is accomplished so quickly and easily that he looks at the camera, obviously expecting to hear "cut!" or get some further suggestion. Nothing happens, and De Niro, momentarily at a loss, tries to come up with more action, a kiss, or something. He quickly succeeds at this as well, and looks at the camera again! The scene still is not cut, and continues to unravel.
Continuity mistake: There is a scene in the film where De Niro and Pesci are in a living room and De Niro is next to the TV trying to fix antenna whilst talking to Pesci. In most of the camera shots between the two guys the antenna often changes position without De Niro moving it.
Continuity mistake: During a scene where the boxer is in his home, you hear an ambulance siren from his window. The siren is a modern siren rather than the slow low to loud sound then back from loud to low type when the movie was dated.