Continuity mistake: When Mugsy takes Bugs into the other room, you can see the door has no handle, but when Rocky draws a gun and goes to see Bugs, a handle appears from nowhere.
Continuity mistake: The view out the back of the barn door when it's first revealed does not match the same view, just minutes later, in the final shot of the film. (01:55:43 - 01:59:12)
Continuity mistake: During the start of the famous "I coulda been a contender" scene, watch Terry's head. When he tells Charlie that "it was you", his head is tilted to the left. In the next shot, it's tilted to the right.