Continuity mistake: When Carlotta brings the plates for the meal they all have a dome cover with a top handle, but when Sebastian runs across the table those handles have changed. (00:54:50)
Factual error: Joe Jackson batted left-handed in real life, not right-handed as Ray Liotta portrayed. He also threw right-handed and not left-handed like it shows when Kevin Costner is hitting him fly balls to left field.
Continuity mistake: Notice Marty's hair in the scene when he's playing "Johnny B. Goode." It's quite larger than when he says, some seconds later, "I guess that you're not ready for it yet." That's because when he says that, it's a recycled shot from the original BTTF, whereas most shots showing he's playing the guitar are newly made for BTTF2. However, Marty's hair is considerably longer in the new shots. (01:27:19)
Other mistake: When Miyagi throws Mike into the light switches, the lights go out but the switches never change position.
Revealing mistake: When Nick is being sucked out of the hole/cave, you can see the wires visible from his waist. (01:20:35)
Plot hole: They go and buy Anne Marie a whole new wardrobe. So, how come in the remainder of the movie she continues to wear her old rags?
Continuity mistake: When the reindeer gets into the house and runs around, it knocks over a TV set. All of the magazines that are on top of the set come crashing to the ground, including a TV Guide with "Get Ready For A Fabulous February" (or something like that) in big letters on the cover. Interesting since the movie is set around Christmas time.
Character mistake: In the finals of Video Armaggeddon the compere keeps making comments such as "Jimmy loses a life and starts over in world two", "Laura finishes world two", "Lucas finishes world two". All three times the relevant person is actually in World 1 - Level 3. In Fact at no point are any of the competitors in World 2 and the only time any of them is out of World 1 is when Jimmy uses the warp to access World 4.
Continuity mistake: When Wallace races to get crackers, check the packet's logo. When the camera angle changes it's different. (00:08:57)
Continuity mistake: The snowman hits his nose with a hammer, completely bending it in half. In the next shot it is suddenly magically straight again.
Continuity mistake: When Brian spends his first night in the underground monster world he goes in wearing a shirt and boxer shorts. But a later scene shows him wearing a shirt, pants, and shoes. He then goes back home and is back in his shirt and boxer shorts.
Suggested correction: It's entirely possible that he was able to borrow a pair of pants while down there.
I just watched the scene where Maurice and Brian pull the pranks to get the kids into trouble and he is in his pyjamas. Later in the monster world he is in a full outfit including a shirt, pants, and shoes. Then he goes back home and he is in his pyjamas again.