Revealing mistake: During the scene when Michael steals the station wagon from Dr. Loomis and the nurse, when she is lying across the seat you can see the passenger window is clean and very much transparent. However in the very next scene where Michael goes to smack his hand on the window, it is now foggy - a side effect of the glass alternative used for the effect.
Continuity mistake: In the beginning, when the doctor is talking to the new nurse for Michael in the car, the nurse is smoking a cigarette, but seconds later she has just lit one up. If she smokes one in 45 seconds then lights up another she is one worst chain smoker I've ever seen. (00:08:05)
Visible crew/equipment: In the scene where Dr. Loomis makes a call to Haddonfield police in a phone booth by the train tracks, you can see a reflection of a crew member in the phone booth glass.
Continuity mistake: In the scene where Laurie comes downstairs after taking a shower, she is at her front door singing to herself and she is looking out a window directly to the left of the door. Then there is a shot of the front of her house outside and you see her exit through the door that had the window next to it, but there is no longer a window there.
Visible crew/equipment: When the camera is zooming in on Laurie in school, the camera's shadow can be seen over the students it passes. (00:15:30)
Continuity mistake: When Michael stabs Laurie in her arm the wound doesn't bleed at all, and there's no blood on the knife either. Then when she kneels down to talk to the kids, and in every scene after that, there's a streak of blood.
Continuity mistake: When Michael is at Tommy's school, there are cars parked across the street. When he gets in the car to leave, they are gone.
Visible crew/equipment: When Laurie is trying to escape from the kitchen, you can see some kind of blue light in the top left corner making it look like it's light from the moon.
Revealing mistake: In the scene where Dr. Sam Loomis is calling from a pay phone warning of Michael Myers return to Haddonfield, a Southern Pacific freight train passes by blowing its horn (you can't see the train in the standard version). While SP trains are quite common in Southern California where the film was made, they don't actually travel through any part of Illinois. (00:19:15)
Plot hole: When Laurie and her friend see the Sheriff in front of the hardware store, he tells them someone broke in and stole "A Halloween mask, some rope, and a couple of knives." Without someone doing a complete inventory of the store, there would be no way to know the specific items that had been stolen, especially when they are such commonplace things as knives and rope in a hardware store.
Suggested correction: Simple, he watched the security footage.
Before shutting off the alarm? Store video wasn't really a thing in a small town store back then.
Continuity mistake: Laurie's hair keeps changing throughout the movie. Her hair changes from wavy to straight while she babysits the kids. It is wavy again when she is going to Lindsey's house, and straight again when she is running back to Tommy's house. It stays straight until Michael starts to strangle her,where it becomes wavy again, having been straight in the previous shot. It all ends with straight hair. Surely all of this could not happen in a matter of hours.
Visible crew/equipment: After Lynda and Bob make out on the couch, they both start to go upstairs. Lynda trips over the dolly track and Bob steps over it. (01:01:50)
Deliberate mistake: The opening camera scene, that's supposed to be shot from Michael's POV as a child, is too high as noted that he's almost face to face with his parents at the end of the scene and then is only mid-chest up to the father when he removes the mask. The POV is also too high as he walks across the dining room and as he approaches his sister upstairs.
Continuity mistake: When Laurie escapes the house by smashing a window pane, the glass shards disappear instantly in the next shot. (01:17:47)
Continuity mistake: After Tommy breaks the pumpkin, he is now walking on the sidewalk without the books that he was holding before.
Visible crew/equipment: When Laurie tries to escape Michael from the kitchen, she breaks the glass. You can see a second hand break the glass in front of Laurie's.
Suggested correction: You are incorrect, but it's an understandable mistake to make because the scene is very dark. It's hard to see, but Laurie actually uses both hands to break the glass... she puts them together and then slaps them through the window in a quick, fluid motion. (If you go through frame-by-frame or in slow motion, it's much, much easier to see.) That's why you're seeing two hands. It's not a crew member's hand... it's Jamie Lee Curtis' other hand.
Continuity mistake: When Laurie goes to leave the key, the door has two intact glass frames but when the view changes there's only one that's almost completely broken. Later when Loomis enters the house, there's two again, with one only being slightly broken. Also, the frame from the inside looks really small when Michael watches, and we don't see planks nailed across to cut out the view from inside, as well as there being a screen door that isn't there from the outside, but is there when the view is from inside. (00:13:35 - 00:36:40)
Revealing mistake: Lynda calls Laurie using a rotary phone yet doesn't even look at what she's dialing. And you can tell she's not actually dialing in the first place.
Continuity mistake: At the start of the film Michael smashes the window, later on at the school the window is intact.
Continuity mistake: Michael breaks the passenger front door window on the wagon when he takes car, a short time later when he's driving in town the window is not broken.