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: In the Tech Noir Bar, the same woman - blonde with a pink or orange dress - must have come dancing with her twin, because while she's sitting behind Sarah Connor when the laser beam is pointed at her, she's also dancing near Arnie. The T-800 moves past her when he sees Sarah Connor and moves to shoot her. (00:35:05)
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 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: Arnold looks up Sarah Connor's address in the telephone book. The telephone book address has 4 digits, but he goes to a house that has 5 digits on it. (00:15:00)
Continuity mistake: The telephone message left by Sarah's roommate changes the two times we hear it. The second time, there is no delay between "Hi there" and "ha ha ha fooled you", while the first time has a delay of over a second. Not only that, but Ginger knocks the phone over when she is initially shot, so it could not have rung while the terminator was there. (00:25:55 - 00:32:05)
Continuity mistake: Kyle loads a shell into his shotgun, then falls asleep and dreams of his past in the future. When he wakes up, he pumps the shotgun, so the first shell should eject, but doesn't. (00:20:05)
Continuity mistake: When Ginger is rooting through the fridge while her boyfriend fends off The Terminator in the bedroom, Pugsley the iguana scares her by knocking some food off the top of the fridge. We then see a close up shot of Pugsley knocking some more food over. In this shot we see him knock over a box of "Harvest Wheats" onto its front and a box of "Honey Grahams" placed on its side and at an angle. We then cut back to Ginger telling him to shoo and then back to Pugsley. In this second shot, the box of "Honey Grahams" is now standing upright and facing the camera and the box of "Harvest Wheats" has completely disappeared. (00:30:40)
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)
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: After Kyle saves Sara from the dance club and has her in the car she tries to get out. Kyle stops her by grabbing her. In one scene he's holding her by the back of her hair, and when it cuts back to him his hand is across her chest. It goes back and forth like that. (00:37:20)
Continuity mistake: After the Endoskeleton emerges from the diesel fire look at his teeth. They're clearly metallic when he stands up and chases after Sarah and Kyle, then when he enters the factory his teeth are white enamel. Then when he's fighting with Kyle they're metal again and finally they turn white after he's blown apart. (01:31:05 - 01:34:20)
Continuity mistake: At the start of the film when we first see Reese arriving, the drunk homeless guy is holding a bottle in his left hand, then the camera continuously switches between Reese's arrival and the old guy, in these shots, the bottle keeps changing hands from left to right, then back to left. (00:06:40)
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: 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: Two large railings can be seen curving around the building corners when the cops arrive at the alleyway to pursue Reese. Those railings weren't present in the shot preceding Reese's arrival; the cops pulling up was filmed in a separate alleyway. (00:06:15)
Continuity mistake: When the Terminator steps into the house to kill Sarah Connor he walks over the thresh-hold however in the next shot he is outside again. (00:16:15)
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: 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 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)
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.