
Continuity mistake: In the scene where the Terminator and John are at the pay phone John picks the gun off the floor, it's cocked when it's in his hand, but as soon as he passes it to the Terminator, it's not cocked any more. (00:47:30)

Continuity mistake: When the T-1000 is chasing John in the black tow truck, after the truck goes off the bridge you can see that the truck has two tall exhaust pipes behind the cab. Then right after the truck hits the 2nd old car it shows a shot from behind the truck and the pipes are suddenly cut off. (00:34:55)
Visible crew/equipment: When Arnie is airborne on his cycle in the canal scene, you can faintly see the wires holding up his bike - from just around his shoulders right before he lands to until it switches scenes. (00:37:15)

Revealing mistake: When the T-1000 is firing out of the hole in the windshield of the chopper, a close up shot shows that there is clear tape around parts of the window keeping all the little bits of glass together. (02:03:15)

Continuity mistake: In the car chase just before the final encounter in the foundry, the T-800 slams on the SWAT van's brakes and the helicopter slams into it, crushing the choppers front. A second later it is in reasonably good shape. (02:04:00)
Revealing mistake: Just when Arnie lifts John onto his bike for the first time, you can see Robert Patrick has been replaced by a stunt driver when he crashes into the wall. (00:37:35)
Continuity mistake: In the bar scene after the biker burns the Terminator's chest with the cigar, it leaves a burn mark. Another biker comes behind him and hits him with a pool cue-the burn mark has disappeared, and then re-appeared in the next frame when he grabs that biker. (00:08:20)

Continuity mistake: When the SWAT van crashes through Cyberdyne's front doors into the lobby, it comes to rest with the rear doors closed. When Sarah and John Connor enter it, it's in a different position and the rear doors are fully open. (02:00:35)
Revealing mistake: Right after the T-1000 has been terminated and the T-800 is "saying goodbye" you can see the face make-up where you can see his metal endoskeleton bending with facial movement as he speaks. (02:25:00)
Continuity mistake: When Sarah is escaping from the hospital there is a scene where the T-1000 walks straight through a metal-barred door. If you look where the doctor is standing you will notice that the T-1000 clearly walks past him after he walks through the door. However, in the next sequence when the T-1000 is shooting his gun, he is way behind him. (00:59:30)
Revealing mistake: When the T800 is driving the police car from the hospital, the outside is a clear projection. (01:06:20)
Ssiscool

Continuity mistake: During the aqueduct chase the amount of damage to the semi-trailer truck changes repeatedly. Damage to the semi's grille is severe, then is not. This happens about three times. (00:35:20)

Revealing mistake: In the scene where John is helping Arnie up after the T-1000 has been exploded and sent to his doom in the fiery pit of molten steel (Arnie is saying "I need a vacation"), you can see how the effects crew haphazardly put on a fake busted mechanical arm underneath Arnie's coat and how it bulges out from his shoulder. You can almost see how they just tied Arnie's arm back behind his back and put a fake arm over him. (02:23:35)
Continuity mistake: When the T-1000 is chasing Sarah, John, and the Terminator in the nitrogen truck, just before Arnie fires the first grenade, a blue car comes between them forming a diagonal line across the road (the Terminator, blue car, truck). After a brief close-up on the Terminator shooting, we cut back to a wide shot, the blue car's disappeared, and the truck's now directly behind him, Sarah, and John; not enough time for them to move like that. (02:01:40)
Revealing mistake: When Sarah, John and the Terminator drive through the fence to escape the mental hospital, it's (quite) obvious that the T-1000 attached to the back of the car is nothing more than a dummy. (01:05:10)
Audio problem: When Arnold Schwarzenegger is being chased by the truck and and pulls John out of his bike,you can hear John scream but if you look closely he doesn't move his mouth. (00:37:35)
Continuity mistake: When the T-1000 has stolen a police-motorbike, you can see this is a highway-bike when approaching the building, but becomes a cross bike when going up the stairs. Easiest way to tell is the engine note and the tread on the front tyre. (01:54:45)

Revealing mistake: When the T-800 is being attacked by the SWAT team in the Cyberdyne building, notice that in most of the shots (i.e. when he is being shot in the face, and also when the camera is behind him) Arnie has been replaced by a dummy. When the T-800 pulls out his gun and starts shooting the SWAT team, it's now back to the real Arnie, and notice how none of their bullets are now hitting his face and body, even though shots are still being fired. (02:00:20)
Daz
Revealing mistake: When the T-800 and T-1000 first begin to fight in the steel mill, the T-800 puts his fist through the T-1000's head causing him to revert to liquid metal form, then as the T-1000 is throwing the T-800 from side to side you can obviously tell that the T-1000 is just an actor wearing a highly metallic mylar suit in some shots. (02:14:10)
Factual error: When the T-1000 is scanning the parking lot in the bar near the beginning of the movie, he scans the lone car parked outside and his display reads "Plymouth sedan." The vehicle he scanned was a Ford LTD Crown Victoria. (00:06:50)
Answer: He didn't steal his clothes, but copied them. He can only copy things that he physically touches. He had to touch the cop to take on his look. Also since the cop was a witness to this ruthless killing machine, it needed to kill him to protect itself from being discovered too soon. The Terminator is an infiltration unit on an assassination mission to kill John Connor. As advanced as it is, it needs as little attention drawn to it as possible. Having the entire police force chasing him down would not be ideal for his goal to get Connor and would inevitably slow him down and risk allowing Connor a better chance of escape. The T 1000 also is an emotionless machine programmed by other machines that are intent on killing off all humans in the future. It doesn't value human life, and if anything has been programmed to regard them as a pest to be dealt with. The cop was a means to an ends and an obstacle to take out. As well, the cop did also posses a weapon, and was the T-1000's quickest way to get his hands on a gun.
Quantom X