Character mistake: In the beginning where they are showing all the newspaper articles, the article uses Michael "Meyers" twice in one article and then back to "Myers."
Continuity mistake: Although I understand the fact that H20 didn't want to include the Halloween 4, 5 and 6 timeline, Michael was burnt to a crisp by Dr. Loomis in the epilogue of Halloween 2, so he should have a fully burnt body. Also Michael was shot twice by Laurie in Halloween 2... He would have at least had scars/damage to his face in H20.
Suggested correction: This is addressed and left unexplained in the film, as Laurie's son doesn't believe Myers could have possibly survived the events of 'Halloween II' but apparently has anyway. We are left to speculate whether 'Halloween II' had truly ended the way we had seen, or if the recent killings were not actually by Myers but a copycat stalker, or if Myers is supernatural, etc. Viewers are free to consider this a bad or stupid choice if they wish, but strictly speaking it isn't a mistake.
Suggested correction: Michael's vision is also fine despite losing his eyes to gunfire at the end of Halloween 2. He can regenerate far better than most people.
Continuity mistake: Jimmy opens the fridge. On the second shelf there are no packages of lunch meat. A few seconds later a pack appears, and shortly after that 4 more appear out of nowhere. (00:04:10)
Plot hole: At the end of the film all the police and ambulance vehicles manage to get into the school, but earlier Keri/Laurie smashed the mechanism that opens the gate.
Suggested correction: There's been a series of murders tied to an infamous serial killer... more than likely the police broke down the gate to gain access. (Which can be done in any number of ways: sawing through the locks, having the fire department dismantle it, ramming through it with an armored vehicle, etc.) They're not going to not come in just because there's a gate they can't open. Also, a quick Google search indicates that often, police are given access codes or ways to remotely open gates at certain buildings (schools, senior centers, etc.) in the event of an emergency. So it's entirely possible they also had a way to open the gate without breaking it down.
Continuity mistake: The word CORONER appears and disappears on the van.
Character mistake: The newspaper article seen during the opening credits dates the Halloween murders (the events of the first and second film) as taking place in 1968, when they in fact took place in 1978.
Continuity mistake: When Sarah is injured and riding up in the dumbwaiter with Charlie's dead body the position of Charlie's head changes significantly between shots. (00:59:57)
Continuity mistake: Just before Michael stabs Laurie you can already see the injury make-up applied to her arm as she swings the axe at him. (01:10:39)
Visible crew/equipment: When the school buses depart from the school for Yosemite you can see the reflection of the crew's various tents and facilities in the buses side windows as they drive past the camera. (00:42:43)
Visible crew/equipment: After discovering John and Charlie in town Laurie drives them back to the school. The front gates are closed so Laurie honks her horn for the security guard's attention. John then get's out the car and as he does so you can see some equipment reflected in his car door just off-screen. There's some kind of large blue object and orange traffic cones definitely visible. None of it is there in wide shots. (00:33:46)
Visible crew/equipment: The first time we are introduced to Charlie and Sarah they are discussing the trip to Yosemite with John. As they walk through the school courtyard pay attention to the glass windows behind them (right side of the screen) and you can see a reflection of the camera and crew following in front of them. (00:17:59)
Continuity mistake: When Sarah is in the dumb waiter with Charlie, she looks down at the cut on her leg, then at him, and he's looking straight forward and up. In the next shot, as the dumb waiter reaches the top, his head is turned, looking at her, and remains that way until she exits and the dumb waiter drops when Michael cuts the rope.