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.
Revealing mistake: After Reese blasts the Terminator with his shotgun while at the Tech-Noir nightclub there should be huge holes in the Terminator's shirt and jacket, but there are none.
Continuity mistake: When the Terminator is washing his face in the motel room after he was wounded during the chase, the tap's valve is showed in different positions between two shots.
Continuity mistake: In the Tech-Noir bar scene, as Sarah is seated at the table and knocks the Canada Dry bottle to the floor, right when she leans down to pick it up, a guy sporting a white suit, white tie with three black tie clips and red pants begins passing behind her from the right side of the screen. In that exact same moment, while she's still bent over retrieving the bottle, the reverse-angle shot captures that same guy in white suit and tie, now dancing in front of her table as Arnold walks up scanning the area. (00:34:20)
Continuity mistake: When Reese and Sarah are fleeing from the Tech-Noir nightclub, right when the Terminator jumps on the car they're driving away in his hairstyle magically changes.
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.
Continuity mistake: When Arnold exits his motel room to kill Sarah's mom at the cabin he has on what looks like a pair of Sperry boat shoes. After he kills and impersonates the mother and heads for the Tiki Motel on his bike he has the black motorcycle boots back on. (01:14:40 - 01:17:40)
Continuity mistake: We see the Terminator remove his left eye in the hotel room and it leaves a wound about the size of the sunglasses lens, in most face shots after that while he is wearing the sunglasses the wound has disappeared and the skin around the eye is perfect when we see that side of the face.