As Allyson is walking with her friends along a sidewalk discussing her grandmother they pass a lawn decoration that is a tombstone with RIP. There is an edit to a wider shot during the same sentence, but now they are passing by a plastic skull positioned in front of a tree that had not been there.
When Dr. Sartain lies on the floor after he is being pulled out of the van by Michael his head is smashed to pulp by Michael his foot. When the cops investigate his body his head is more or less recomposed back together.
When Aaron is pumping gas at the gas station, the pump is not actually pumping any fuel as shown by the display being blank. When he finishes pumping gas later, the pump shows the gallons and cost on the display like normal.
When Sheriff Hawkins enter the house on the domestic disturbance call, he yells out "Haddonfield Sheriff's Department". The patch on his jacket says "Warren County Sheriff". Haddonfield is an incorporated municipality and would not have a county sheriff patrolling but rather a police chief, as sheriffs are county level law enforcement and the municipal police would be the Haddonfield Police Dept.
Sherriff Hawkins was a deputy in 1978. Let's assume that he was just barely 18 at that time (which is also unlikely) that would make him 68 years old now. Ususally he would be retired by this time instead of still being on active duty.
When Michael Myers walks around Laurie's house, the view from the basement shows gaps, dust and even his footsteps through the floor. Earlier the floor was shown to be consisting of square floor tiles without gaps.
Near the end of the film the two police officers guarding Laurie's house are requesting backup after finding a murdered police man (= the doctor) near the police vehicle, which stopped a short distance from them. After the climax, with Laurie's house now on fire, Laurie, her daughter and her granddaughter hitch a ride on a pick up truck, yet backup is nowhere to be seen.
The goof item below may give away important plot points.
Incorrectly regarded as goofs
At one point, Laurie Strode mentions that Michael Myers killed five people in 1978. That would be incorrect because he killed only four people which includes the truck driver, Annie, Linda, and Bob. However, during this scene, there is no mention of the year 1978. Laurie simply says that Michael killed 5 people, and this is including his sister Judith.