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 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.
Continuity mistake: When Loomis and the sheriff are surrounded by the teens dressed like Michael Myers, Sheriff Meeker say's "If I catch you it's a weekend in jail" indicating that it's a Friday. Halloween was actually on a Monday in 1988.
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.
Audio problem: When the head of the Federal Sanitarium gives over control of Michael to the Doctors from Smith's Grove, he says, "I can safely say that Michael Myers is in your hands." If you watch his lips, you can see that the sound of the words and his lip movement is way out of sync.