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.
Ssiscool
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)

Revealing mistake: After Reese finishes battering the Terminator with the pipe, the Terminator strikes back at him. Just before the camera angle changes to show us the pipe dropping on the floor, we get a close up of Reese's face. It is a stunt double, not Michael Biehn. (01:35:10)
Character mistake: When Kyle steals the police officer's gun and asks him what the date is, the officer replies "12th, May, Thursday". The film is set in 1984. May 12th, 1984 was a Saturday.

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)
Phil C.Visible crew/equipment: As the Terminator moves his right arm whilst in the press, you can see a crew member, behind the Terminator, move in the area of the picture where its arm was. (01:34:05)

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)
Revealing mistake: In the second future war sequence. At the end of the HK/car chase, the gunner in the car has been replaced by a very obvious dummy. (00:19:55)

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)

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)
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: 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)
The-Immortal
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)
Revealing mistake: When the Terminator goes in to the Alamo gun store, scene of the famous "Uzi 9 millimeter" quote, the man turns to get something off the shelf and Arnold takes a shell out of the box on the counter. It is an already fired cartridge: the dimple in the centre shows it.
DeadlockFactual error: Sarah and Lieutenant Traxler both state that Tech Noir, the club Sarah is in, is on Pico Boulevard. After the gun battle inside the club, Sarah leaves with Kyle and they run a short distance down the alley behind the club before getting into a car. The Terminator jumps on and falls off as soon as the car is out of the alley. When the cop calls it in, though, he says he needs an ambulance at 7th and Broadway. Even assuming Tech Noir was on the corner of Pico and Broadway, that is still about 3/4 of a mile away from 7th and Broadway, so there is no way that was the intersection just outside the alley.
bixxell
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 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)
Ssiscool
Revealing mistake: At the end of the film, at the split second we see the ambulance workers zip up Reese in the bodybag, his right eyelid flinches a bit. (01:39:45)
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)
Mark Cuss
Chosen answer: Since terminators cannot self-terminate, only one very likely possibility comes to mind: it would have hidden itself away somewhere known to have remained undisturbed in the years between the termination of Sarah Connor and the start of the war, at which point it would rejoin the war effort.
Phixius