Revealing mistake: Visible wires holding up Will when Michael holds him in the air.
Continuity mistake: When Kerrie comes back from lunch with Adam Arkin she is in the car with Josh Hartnett and Adam. She turns into the school driveway and it clearly shows that her window is up but in the next shot when she calls for Ronnie her window is down.
Continuity mistake: When Jamie Lee Curtis hits Michael Myers with the van and they go over the cliff, you can see that the back doors of the van swing open, but when they get a frontal of Jamie going down the cliff in the van, the doors are shut, this happens about 3 times before the van finally stops.
Continuity mistake: When Sarah is fleeing from Michael, she gets into the delivery vehicle with Charlie, who is dead. His eyes are open, but then they are closed.
Continuity mistake: When Will and Laurie are in the hall, it is Michael who comes up the stairs, as you can see the mask and hair. It's not until they cut away to Will and Laurie, then back again, that "Michael" becomes LL, and gets shot.
Continuity mistake: In the yearbook photo of Laurie it says class of 78. She just started her senior year a few months earlier, so she would be class of 79.
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.
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 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.