Continuity mistake: When Cole is shouting "Why are these chains on me?" you can see his face is dry. When it cuts he is drooling a lot. (00:13:45)
Continuity mistake: When Cole tells Dr. Railly he's been in an underground prison, you see him grabbing the bottom of the chain. When it cuts, he isn't holding the chain at all. (00:13:55)
Continuity mistake: The boy does not wear teeth braces at the beginning of the movie, but in the second flash-back (just after the psychiatrists' board meeting) the boy does. (00:25:30)
Continuity mistake: When Goines is jumping on the beds, he rips up a pillow and feathers fly everywhere. The amount of feathers in the air changes between shots. (00:27:50)
Audio problem: When Cole and Railly discover the twelve monkeys symbol on the walls, Cole grabs Railly's arm and shouts "Hey!" twice, but his lips don't move the second time. (00:57:45)
Revealing mistake: The paint in the "we did it" lettering in the roaring bear scene runs "downwards," according to the camera position, not according to the vertical of the shot buildings. (01:51:15)
Suggested correction: While yes there are slight angles involved, considering this was most likely a physical prop on-set, the direction of the camera tilt wouldn't be a factor. The direction the paint runs in doesn't seem wildly inconsistent with what would happen when painting something like that.
Continuity mistake: In the final scene in which a man is shot in the airport (part of this scene actually recurs throughout the movie), the psychiatrist woman leans over him to hold him as he dies. From one angle, he reaches up to her face and his hand is clean. In the next angle, his hand is covered in blood as he touches her face.
Continuity mistake: When Cole (Willis) asks Dr. Railly (Stowe) to turn up the radio as they are driving to Philadelphia, the camera cuts to her hand working the radio. The numbers on the radio clearly move as if being tuned, not the volume being raised.
Other mistake: The bear is lit by a flashlight before Cole actually picks the flashlight up.
Continuity mistake: At beginning of the movie James Cole goes on a volunteer mission. Look closely: snow appears on his space-helmet before he removes the manhole cover to reveal the snow.
Continuity mistake: After James Cole finds out about the Army of the Twelve Monkeys in 1996 and he is driving with the psychiatrist, they approach a turn in the road. You can clearly see the turn, but the doctor does not turn the steering wheel.
Revealing mistake: When Dr. Railly is tied to the bed in the motel, her bonds are not very secure. In her struggles, she very nearly frees her right foot, by accident.
Factual error: The bullet removed from Cole's leg is totally undamaged. Even a full metal jacket bullet will be squashed when it hits a person's leg (and stops inside the leg).
Audio problem: Just after Goines is talking about germs, he says he can get help Cole get out. Cole then says "You know how to get out of here?", but his lips say something else.
Continuity mistake: In the taxi on the way to the airport, the shot looking through the windshield shows the steering wheel turned ninety degrees even though they are travelling in a straight line, when shown from the back seat, the wheel is straight.
Continuity mistake: Near the end when James meets up with Jose at the airport, at first Jose has mirrored sunglasses but later they are mirrored with a glaze to them. Probably to avoid crew reflections.
Continuity mistake: In the scene where Cole is restrained in the bed with the comforter with teddy bears on, the position of the comforter changes between shots. He raises his head and that makes a crease in the comforter. In the next shot the comforter is straight again.
Continuity mistake: When Bruce Willis is tied in the bed with the painting hanging over him, the doctors pull a teddy bear blanket up to his chin. Then there is a cut to a closer shot of Bruce raving and the blanket is nowhere to be seen.
Plot hole: At the end the police shoot Cole while he was chasing Dr Peters but the police do not stop Dr Peters and question him as to why a man was chasing him at the airport with a gun, instead he is unchallenged and allowed to continue his journey.
Suggested correction: There is no connection between Cole and Dr. Peters, nobody knows he is specifically chasing him. Dr. Peters is beyond the gates and on his way into the plane so unless they want to stop the entire flight, which is unlikely, he is left alone. Perfectly reasonable.
Cole is chasing a man and Dr. Peters is running away (and knocking people over in the process). Further, they were screaming "there he is...stop him he's got a deadly virus" and pointing at Dr. Peters. Highly unlikely they would have let the plane depart.
There was a dude with a gun, a lot of people were running, panicking. Perfectly reasonable reaction from Peters. The police were after Cole anyway, so the attention was on him, not on Peters. And as I said, Peters was already past the inspection, so he was where he was supposed to be and there was no reason to stop him.
Not to mention that Dr. Railly can also corroborate the reason Dr. Peters is being chased.
Dr. Railly can corroborate the reason Cole is chasing Dr. Peters. When she points out that he is even on the front page of USA Today with a Nobel Prize winner, I think they'd definitely investigate.
The shrink was still alive and seemed to give up quickly on her mission to stop a virus from killing billions. Like she just let them take her while she remained silent instead of continuing to scream that he had a virus so Cole died in vain. And they would know why he was chasing them because all they would need to do was ask him.
Her concern was with Cole, she tries to protect him throughout the movie. After Cole is shot she knows there is no way they let her continue the chase, all she cares about is Cole. Cole is being chased by the cops, no reason for them to believe what he is yelling, no reason to believe her either, since she is as an accomplice.
Other mistake: When Catherine is seen from a distance spray painting the wall, she is holding the spray can about 20-30 cm from the wall. But that is way too far to make letters. The paint will be disbursed over a wider area, and not make precise lines.
