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)
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.
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.
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.
Continuity mistake: In the beginning of the movie, the psychiatrist has silver shoes on. However as she rushes to meet her new patient (James Cole) at the local police pound, they appear to be black.
Continuity mistake: Before Cole returns to his own time for first time, he has several wounds on his head and face which disappear when he talks with the bosses.
Answer: The tattoo is for the movie. It is his prisoner identification.