Continuity mistake: When Karen is at the the Hostess party, and Jimmy Conway's wife is talking about Jeanie's family, if you look at the lady she's applying make up to, she crosses begins to herself twice. One when the camera is one her and Jimmy's wife, then again when the camera is just on her.
Other mistake: When we see the shot couple in the pink car, there's blood spatter inside the windows and windshield, so that means the windows were up when they were shot, and they were shot in the car. It makes no sense that neither the windshield nor the windows are broken. If Jimmy shot them from the front, he would've had to have shot them through the windshield. If he shot them from the side, he would've had to have shot them through the window.
Suggested correction: This one is pretty weak. Jimmy knew them. He could have easily walked up to the door and opened it, as if to admire the car, as if to talk, or for any other reason, shot them, and closed the door.
Factual error: When Henry and Jimmy go to Morrie's to collect jimmy's money, Morrie's commercial seems to be running on a loop, presumably via VCR. VCR was invented in 76 and available in the US a year later. This scene was before then.
Continuity mistake: When Tommy is shot, there's no bullet wound in his head, but in the very next shot, there is. And we don't see the moment of impact, that wound was always there in that entire second shot.
Continuity mistake: When Henry beats the neighbor kid and then passes the gun to Karen, her knit sweater is sometimes on one shoulder and sometimes on both arms.
Other mistake: When Tommy kills Stacks, after he leaves the apartment, they re-enact the murder from a different camera angle in slow motion, where we see Tommy's face. Right before Tommy starts shooting, we can see blood stains on the wall already.
Continuity mistake: When Tommy is shot, Tuddy is holding his shirt, but in the very next shot, he isn't, and he's much further away from him.
Continuity mistake: After Tommy shoots and kills Spider, Henry sits back up and puts his hands down from covering his ears twice.
Continuity mistake: After Karen's been harassed by her neighbour, Henry drives her home and tells her to walk home. When Henry steps out, she's nowhere to be seen. She couldn't have walked all the way to the house in that short time. She couldn't have run, either, being as weary as she was.
Factual error: Unless Henry was intoxicated or heavily medicated during his sleep, it would have been impossible for Karen to have climbed on top of him in bed, point a gun at his head, without him ever feeling her body on top of his.
Revealing mistake: Young Henry's eyes are distractingly bad with obvious contacts that look really fake.
Audio problem: When Billy Batts is explaining to the guys about Tommy's shining his mouth doesn't match up to the words.
Audio problem: When Janice is handing the dog to Tommy at her apartment he's talking but his mouth isn't moving.
Continuity mistake: When Karen is over Henry pointing the gun at him, the trigger is pulled all the way back. The gun also goes from blue steel to silver.