Continuity mistake: Throughout the car chase shots where the Terminator is in the stolen police car, the car's rear view mirror is round. After the car crashes into the wall in the tunnel, the rear view mirror is square. (00:49:35 - 00:50:20)
Continuity mistake: In the scene in the apartment, where the Terminator cuts the flesh away from his damaged eye, he picks up a hobby knife that has a blade attached. In the next shot, as he lifts the knife up toward his eye, the blade has disappeared. Then in the front-on shot the blade is back again. (00:52:35)
Continuity mistake: When Kyle is in the police station being interviewed by the psychiatrist, watch where he says the line: "It's just him... and me", it appears different later in the film when the psychiatrist is showing the tape to Sarah. The first time, Kyle has his head turned up and to his left and on the tape, his head is facing straight as he says the line. (00:54:25)
Continuity mistake: When the Terminator says "I'll be back" he walks out of the police station. The cop inside the building looks out of the window, looks very surprised, and you can see the headlights from the car shining on the cop's face. When we see the car just before it comes crashing through the building the headlights aren't on. In the next shot of the cop the headlights are still shining on him. (00:57:25)
Visible crew/equipment: In the police station, you see all the police officers running to get the automatic weapons. There is one shot where a red dot is seen to be following one officer (and it's sometimes on his back). No cops are facing the back of this cop, the Terminator is not around this part of the station, so it must be off the camera. (00:59:10)
Factual error: In the scene after Arnold says "I'll be back", it shows the desk cop writing a report with a pencil. Any public servant or corporation knows, reports are only written with BLUE or BLACK INK... NEVER with a pencil. (00:59:15)
Continuity mistake: When the Terminator enters the police department and he bends over to say "I'll be back" you can see through his shades and he has both of his eyes, despite cutting one out in an earlier scene. (00:59:35)
Revealing mistake: When the Terminator takes out his "fake" human eye, he looks into the mirror. It is very obvious it's a dummy: 1) He has unnatural movements. 2) His skin is a lot paler, and not shiny. 3) His hair style has changed. It's easier to tell in the following shot, as he looks closer to the mirror that he's changed back to "real." (00:59:55)
Revealing mistake: When Arnie drives through the police station, the cop is just sitting there. Not only that, his skin is a lot paler. It is too easy to see that it is a dummy. (01:00:00)
Audio problem: When the Terminator breaks into the police station, he has a Franchise SPAS 12 semi-automatic (or selectable pump action) shotgun in his left hand, and an Armalite AR 180 machine gun in his right. Before he kills the power in the building, he comes to the end of a hall, points his shotgun through a doorway, and shoots. A machine gun sound is used for the blast, instead of a shotgun sound. (01:00:28)
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)
Suggested correction: He's definitely not giggling and I wouldn't call it a smile. Maybe he's grimacing, but I seen him just wincing at the situation he's in. At best you could say he's a bad actor, but poor acting isn't a valid movie mistake that I know of.
Continuity mistake: In the scene where Arnold is turning off the power in the police station he gets shot by a cop and jerks forward. But every other time he is shot he does not even twitch. (01:00:55)
Continuity mistake: When The Terminator is searching through Sarah's address book in his apartment he has flies on him. There is one on his forehead, but when the janitor knocks on the door, the Terminator turns his head towards the door and cusses at him but there is no fly on the forehead. When he turns back and continues reading the fly is again on his forehead at the same exact place on the forehead. (01:14:05)
Continuity mistake: After the Terminator discovers Sarah's mother's address in the little address book of Sarah's, the next shot shows the Terminator leaving his room and going to Sarah's mother's. In that track shot down the hall look at the Terminator's shoes. He's wearing white trainers instead of the black boots he wears for the whole other time in the film. (01:14:40)
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: The Terminator loses the flesh around his left eye early on, but at mom's cabin you can see his backlit left eyelash blinking. (01:16:50)
Continuity mistake: When Kyle and Sarah leave the motel in the pickup, they ram the Terminator before they go, and you can see the bull bars on the front are damaged. When the camera shows the front of the pickup during the tunnel chase sequence, the bull bars are undamaged. (01:20:25 - 01:22:00)
Continuity mistake: In the tunnel scene we see Sarah drive past the 2 lorries. They then meet, making it impossible for the Terminator to get past. Angle changes and the lorries still haven't met yet. (01:21:00)
Visible crew/equipment: When Kyle and Sarah escape in the pickup truck, the Terminator chases after them on a red motorcycle. The camera does lots of shots of what's behind Kyle and Sarah and what's ahead of them. When they overtake a truck, you can see headlights following and shining on the back of their pickup. These are the camera crew's lights, as the Terminator's motorcycle is too far away, and previous shots have shown there are no other vehicles around them. (01:21:40)
Revealing mistake: When Arnie is being pulled under the semi-truck, his foot is caught and the green-colored dummy leg is revealed. It can't be a special effect sock since green screening was not in practice in the early 80s. (01:23:05)
Suggested correction: I have literally just watched this scene, you can't see his eyes at all. Even with the brightness turned right up. You can see the outline of his eye sockets but no eyes. Yes, we should be able to see the red of the missing eye, but we don't know if the Terminator has the ability to turn this on or off at will. With the technology available at the time of the films release, one definitely wouldn't have been able to tell any difference.
Sorry to disappoint you, but both his eyes are visible under the shades. So yes, it IS a continuity mistake after all.