(at around 1h 26 mins) When Michael climbs up the attic steps to get Jamie at the end, we see and hear Jamie whisper "Rachel, help me." Then she whispers "Help me." a second time, but her mouth does not move.
(at around 11 mins) When Rachel and Tina are giving Jamie the costume gift at the clinic, Rachel giggles & Tina begins to mimic a trumpet. Then suddenly a loud scream is heard, yet neither Tina nor Rachel seem to have made the sound.
(at around 21 mins) When Loomis and Meeker are talking down at the station, Loomis recalls the events of the first movie saying "my memory goes back 12 years." Since Halloween 5 is set in 1989 and the events of the first movie were in 1978, he should have said "11 years."
(6 minutes into the movie) Jaime has the dream about killing her mother in Halloween 4 (The Return of Michael Myers.) Her mother only screams one time in the fourth movie but the mother then screams more than one time in the dream.
(at around 1h 25 mins) Rachel's body is not sitting in the chair at the top of the attic stairs when Jamie first walks in. Then, Jamie turns around and finds Rachel there. Later, as Michael chases Jamie down the stairs, Rachel's body is missing again.
(at around 48 mins) Deputies Tom and Nick take Tina to the Tower Farm party in a Chevrolet Caprice patrol car. While they are on stake-out there, they are suddenly in a Ford LTD-Crown Victoria. After Michael kills them and steals the car, it is a Caprice again.
(at around 52 mins) When Tina, Sammy, and Spitz enter the barn to see the kittens, Tina's hair is in a high pony-tail. In the next shot, as she climbs under the rails to get to the kittens, her hair is down. Previously, as she was getting ready for the Halloween party, her hair was in a high bun.
(at around 36 mins) Outside the Quick Food Mart where Spitz works, Mikey, who is wearing round sunglasses, is polishing his black Camero. Tina attempts to surprise him by putting a mask over his head. Annoyed, he pulls the mask off and tosses it into the back seat of his car; he is still wearing his sunglasses. There is a jump cut to a POV on the opposite side of the car. Mikey is no longer wearing his sunglasses. As he sits down into the driver's seat he grabs his sunglasses from the backseat near where he tossed the mask and places them on the dashboard of his car.
(at around 1h 3 mins) When chasing Jamie and Billy in the car, Michael's position while driving the changes between the driver's seat and the passenger seat. (The DVD commentary revealed this is because the shot was filmed with the car being driven towards a mirror)
At the beginning of the film, we see Jamie realize that Michael Myers is alive. She grabs her chalkboard & writes "He's coming back." on it. Yet a few scenes later, Loomis is demanding that she write what she knows about Michael Myers. Yet the chalkboard & its message are never seen again.
As with the previous film, Sheriff Meeker and his men are shown working at the Haddonfield Police Department rather than the (Warren) County Sheriff's Department, which are two separate law enforcement agencies. The station itself, patrol cars and uniforms all incorrectly refer to "police" rather than sheriff. While in reality the town could have both, it is clearly established in the film (and those before it) that Meeker is in sole charge and thus there should only be a sheriff's department.
We see the police, along with Jamie and Dr. Loomis, set up a stakeout at Michael Myers' house. But a few scenes later, we see that Michael Myers has an attic full of dead bodies. Why didn't the police find these when they searched the attic before the stakeout?