Audio problem: In the scene where Sharon Stone is talking to Joe Pesci about how De Niro had his guys beat up James Woods, at one point Sharon Stone says, "Oh C'mon." If you look closely her mouth doesn't move at all. Also if you listen closely, that line comes out on surround sound. When she continues her line it comes out on mono. It was obviously recorded.
Audio problem: Ace yells "come with me now" over and over while dragging Ginger out of the house after overhearing her trying to have him whacked. DeNiro's lips are not moving while he's yelling.
Audio problem: When Nicky and Frank rough up one of their debtors, Frank tells him to smarten up, but his mouth doesn't move. (00:31:55)
Audio problem: When Nicky is at the airport having his suitcase searched by Customs, he says "If you find any cash in there we'll whack it up with ya" but his lips don't move in unison with the sentence. (00:27:50)
Audio problem: When Pat Webb is reading aloud the newspaper article about Sam Rothstein, his lips don't match when he begins the sentence reading "the Midwest bookmaker", and also the audio sounds spliced in. (01:31:15)
Answer: Frank Rosenthal (the basis for Sam Rothstein) and Tony Spilotro (the basis for Nicky Santoro) were both from Chicago, so that is likely "back home".