Continuity mistake: In the scene where Sarah and Kyle are escaping in the car they found in the alley after leaving the nightclub, Tech Noir, we see Arnie jump onto the hood of their car in flames. While he is in mid-air during the jump, he is on fire but as soon a he lands (the next shot) the flames are gone. (00:37:35)
Continuity mistake: When The Terminator's stolen police car is shown up close in the parking structure, the motto on the left side of it reads "to care and to protect." After the car crashes, you can see the motto on the left side again, but this time it reads "Dedicated to serve." The car's trim and position/orientation/color of the police emblem change as well. (00:45:50 - 00:50:20)
Continuity mistake: When The Terminator's stolen police car is shown up close in the parking structure, look at the police logo. After the car crashes, you can see the logo has flipped. (00:45:50 - 00:50:20)
Continuity mistake: After the shootout at the disco, there is a car chase. Towards the end of this chase, they turn a corner and Kyle smashes into the police car, veering it off to the right of the screen. If you look closely at Kyle's car as he hits, you can see FIVE shotgun holes in the side of the car. However, a few shots later, Arnie is firing at the same side, but there are only TWO shotgun holes in the side of the car, with Arnie just making the third hole with that shot. (00:47:10)
Continuity mistake: Just before Kyle exits the car park, he rams the police car driven by the Terminator into a parked car, and you can see the front left corner of the police car is damaged. In the next shot when you see the police car exit the car park, the damage has gone. (00:48:30)
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)
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)
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)
Continuity mistake: When the tanker explodes near the end, the Terminator gets out of the truck, then falls to the ground face-first, in an open area. Then he rolls over onto his back, lying prone, and stops moving. When the endoskeleton rises a minute or so later, however, it gets up as if it had been hunched over, face down - and several pieces of the truck's wreckage fall off of it as it rises, as if it had been covered by falling metal. (01:28:45 - 01:31:00)
Continuity mistake: Every shot of the semi truck shows it has single round headlights, but after it's been blown up and the Terminator falls out of the cab, you can see that the truck has now got twin round headlights. (01:28:45)
Continuity mistake: When the tanker explodes near the end, the Terminator gets out of the truck on the left-hand side of the cab, and falls to the ground. When the endoskeleton arises minutes later, however, it is on the opposite side of the cab (Sarah approaches Reese from the right side, and the endoskeleton arises in the background). (01:29:25)
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.