(at around 15 mins) When Dr. Loomis & Dr. Hoffman are in the mental hospital, Dr. Hoffman answers the phone. He says, "I see. I see, thank you," but his mouth movements don't match the words. We then hear him yell, "Loomis! Loomis!" but he is clearly not actually yelling.
(at around 1h 7 mins) The wall behind Michael changes as he takes the gun away from Brady. First, there is a solid wall with decorative hangings, then there is a shot of the front door, then the solid wall again.
(at around 18 mins) The blue sedan Dr. Loomis parks at the pumps outside the gas station is different than the one that blows up minutes later in the same location during a fire. The vehicle he parks is a 1982-1983 Chevy Malibu with four headlamps and one kind of grille. The vehicle that explodes in the fire is a 1980-1981 Malibu with two headlamps and a different grille.
The burn scars on Dr. Loomis' face change periodically throughout the movie. There is a dramatic change from when he is riding in the truck with the preacher on his way to Haddonfield compared to when he arrives and comes into the police station.
(at around 47 mins) When Jamie and Rachel get into the cop car and Sheriff Meeker drives off, you see Michael Myers standing in the road. Right before the scene ends, crew making the smoke blow are visible on the far left of the screen.
(at around 30 mins) When Dr. Loomis is hitchhiking down the road and the preacher picks him up, mountains can be seen in the far distance of the direction that they're traveling. There are no mountains anywhere in the state of Illinois.
(at around 14 mins) When Jamie and Rachel first discuss going for ice cream, Jamie asks, "Double scoops?" and Rachel agrees. (at around 24 mins) After school, in the car, Rachel asks Jamie whether she wants to go to the discount store or Dairy Queen. Dairy Queen serves soft-serve ice cream, which cannot be scooped.
Michael Myers had been at Smith's Grove - Warren County Sanitarium prior to his escape in Halloween and was being transferred to that location at the beginning of this movie. The patches on the medical personnel say Smith's Grove, but the ambulance is labeled as Smith Grove.
(at around 49 mins) Deputy Logan, who was left at the Carruthers' house to wait for the family to get back home, runs out of the house to his patrol car. He gets on the CB and tries to get in touch with the sheriff on the radio. After getting a response, he says he "just heard about the station", at which point, the sheriff tells him to head over to his place. This was after Michael threw "Bucky", the electrical worker, into the electrical wires and put the whole town in the dark. Logan couldn't have heard about what happened from inside the house, as he had to run to the car to get to his radio.
(at around 1h 10 mins) When Rachel is on the roof of the house and fighting Michael, she slides down the roof and slams into the chimney. When she does, the "brick" chimney flexes as though it's made out of thin wood.
(at around 45 mins) After the power goes out, Jamie is on the sidewalk and hear's Rachel calling for her. In the background, you can see tulips getting ready to bloom. Filming was obviously done in the spring rather than the fall.
Michael throws a man into the power grid, effectively killing all of the power in Haddonfield. Even though all of the houses are completely dark, there are inexplicable sources of light that are too bright to be the moon coming from behind trees and buildings, as well as shining in through windows from angles that would be impossible.