Plot hole: When the deputy arrives at the sheriff's house, Michael gets out and leaves the door open. The deputy comes out to the car and sees it open. And he thinks nothing of it, despite knowing he didn't open it. Logic would say, "Well someone else opened it."
Plot hole: Near the end of the movie, Jamie and Rachel are being taken down the highway to safety by the vigilantes when Michael climbs into the back of the truck from being underneath it. Michael then struggles, stabs, and violently throws two of the vigilantes from the truck, and the third vigilante, standing only inches from the other two and still holding guard in the back of the truck, appears to see or hear none of the commotion. Impossible, even for horror films.
Plot hole: At the end of Halloween 2 Michael is completely engulfed in fire for several minutes. Even if somehow he was to survive he would be covered in scars. When we see him at the beginning of part 4 he has a few small scars on his arms. Same with Loomis, he has a few small scars on his arms and one on his cheek despite being in a gigantic explosion and fire. Obviously this was done so they could bring the 2 characters back but it still makes no logical sense.
Suggested correction: Michael has the supernatural ability to heal as shown when he's shot in the eyes at the end of Halloween 2 because in this one he can see, as for Loomis it's possible he was blown into another room or into an area into the room where the flames couldn't reach him, no mistake.
Michael does have some scars though. If the excuse that he heals is the reason he doesn't have more than all of them would be healed after 10 years. Also Loomis was in the same room with Michael, even if Loomis was blown into another room he would have been engulfed in flames and would have been either dead from the shock wave or still burned worse than he is in part 4.
Suggested correction: This one's tough. On the one hand, this is intentional and if it were released today I'd chalk it up to being a (very) soft continuity reboot and that in this film the explosion was simply not as severe as it was in Halloween II. On the other hand, in the context of its release era, and just by watching you can sort of tell they were hoping viewers either had a fuzzy memory of Halloween II or were willing to just go with it. I think I'll err on the side of the former, but it's interesting.
The original script contained an opening scene which showed how Dr Loomis was blown out of the hospital. They had no enough money, so that scene was never shot.
Plot hole: At the end of Halloween II Dr Loomis blows up the room. Since he was inside the room when it blew up in flames, how did it not kill him? And that bad of a fire only scarred one side of his face and one arm and hand?
Plot hole: Toward the end, when Jamie and Rachel are being taken to safety by the vigilantes, Michael suddenly climbs over the back of the truck and slays all the guys one by one. There is no way he could have been 'hiding' under the truck as he was still deep inside the school when the truck sped out of the lot and down the road. Obviously added for dramatic effect at the end.