Continuity mistake: In the end, when Michael has grabbed Karen's ankle and is trying to pull her down into the basement, Allyson grabs a knife off the floor and stabs him. However, if you watch very closely, you can see she's already holding the knife in one shot before she grabs it. (It's the shot right before Laurie screams "I've got you!" to Karen.) You have to pay attention because it goes by quickly, but you can see Allyson lifting the knife into frame for a split second, even though she doesn't pick it up off the floor until about 15 seconds later.
Other mistake: The officers working at the Smith Grove Sanitarium have "police" on their uniform patches. When Michael Myers was boarding the bus to be transported to a different sanitarium the bus had a Corrections Department decal. Since corrections officers run prisons and jails along with sanitariums, the uniform patches should have said corrections, not police.
Audio problem: At the babysitter house, her boyfriend Dave goes out and finds a motorcycle in the garage to the side of the house. He goes in and starts it, revving up the engine loudly. Several shots while he's doing this show the babysitter and the boy sitting in the boy's room reading and they are unable to hear the motorcycle that's blasting its engines loudly. However, moments later when Michael stabs her in that room and she screams, he is able to hear her scream through the house, through the closed front doors, through the yard and into the garage where he was trying to pick the motor cycle back up. How was he able to hear her scream through all that but they couldn't hear the bike which was considerably louder?