Continuity mistake: When Dr. Loomis is thrown through the window by Michael Myers in the school notice that Myers' hair has strangely turned white. The next shot Myers' hair has gone back to being brown. This is more evident in the widescreen version. This was due to a reshoot. Originally the film was going to go with the white haired wig, but then changed to the dark hair wig. Obviously one scene was missed in editing.
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.