Revealing mistake: When the Terminator invades the police precinct to kill Sarah, there is a part where he shoots a cop in the butt with his shotgun (right before he short circuits the building's wires). If you pay attention, the cop is smiling and giggling as he takes cover - before he is blasted. (01:00:45)
Revealing mistake: In the scene were Kyle and Sarah are speeding away from Arnold in the truck, Arnold starts shooting the truck with Kyle driving. When Sarah and Kyle decide to switch (passenger, driver), the camera shows them switching but there is a stuntman in place of Kyle. If not he has gained some weight in the cheeks and grown a big mustache during the course of 2 seconds. (01:24:30)
Other mistake: Why does the Terminator have a HUD (Head-up-Display) or a GUI (Graphical User Interface)? This is a stupid mistake in many movies with cyborgs or androids. A machine itself does not need a HUD. A HUD is an interface for humans to help us interact with machines. A machine does not need a graphical interface to interact with itself. A machine can interpret the reality around internally using machine code within its CPU using zeros and ones. There is no need to project a HUD in the eyes of the terminator. (of course it looks cool and the viewer gets the information that the Terminator is a machine, but in reality it would be - let's say - a stupid redundancy to build in a monitor into a camera).
Continuity mistake: When Sarah is sitting in the bar after talking with the police, there is a drink in a glass on the table in front of her. The scene cuts away and when it cuts back, it is a small bottle, not a drink glass. (00:33:45)
Plot hole: When Sarah is at the police station, the chief tells her something like, "Your mother will be here in a little over an hour." Meaning she is already on her way there. The Terminator reads the address book to find out Sarah's mother is at Big Bear. At the hotel, Sarah is talking to her "mother" (the Terminator). If her mother was on her way to the police station, why is she still at the cabin?
Revealing mistake: In the scene where the tanker explodes, we see the cabin of the truck getting blown up. Then in the next shot, we see no flames have even reached the cabin, and it explodes again, this time with flames.
Continuity mistake: When Reese and later the Terminator go through the phone book to locate Sarah Connor, the second Sarah is listed as Sarah Ann Connor. Later, when Traxler and Vukovich are discussing the death of the second Sarah, Traxler reads the name on the police file as Sarah Louise Connor.