Continuity mistake: Anderton's wristwatch is an Omega Speedmaster X-33, but it shows a Bvlgari display when he looks at it for the countdown to the murder he is to commit. When he's not looking at it, the watch can be seen with its original Omega face. One example of this is in the tub scene where one of the spyders is peeling off Anderton's eye bandage. The watch shows its Omega display (white hands on an LCD digital background). Omega's developer of the X-33 told me that this was a major legal battle for them.
Continuity mistake: Anderton is driving Agatha aka the Pre Cog in his car after kidnapping her from the Temple. She is complaining that she is cold so he takes off his jacket and puts it on her shoulder and body. The next shot is from outside the window looking at her and the jacket is down on her arm. The next shot is back to Anderton and the jacket is on her shoulder again. In the final shot of the Precog, the jacket is on her shoulder.
Trivia: On the "subway" train, the man holding the USA Today paper is Cameron Crowe, and the woman in the seat behind him on his left is Cameron Diaz. Because "Vanilla Sky" and "Minority Report" were so close in shooting, the two directors (Crowe and Spielberg) agreed to put themselves as cameos in each other's films.
Continuity mistake: When John and the other precrime agents go to arrest Howard Marks, they stand in a group trying to figure out which house is the right one. A couple of shots later there's a wide shot of John from behind with nobody else there, and a couple of shots later still, the agents are all in a group again.
Continuity mistake: In the scene when Anderton escapes out of the Maglev Car, we see him jump into a room full of gymnasts. He is on the floor with his legs up in the air, then we see him lower his legs. Yet, in the next shot his legs are back in the air again and we see his legs go down again.
Continuity mistake: At the start, when John Anderton is going to arrest the man who can't see well without his glasses, he his trying to figure out which house the killer is in. While looking around, his helmet is fastened tightly around his neck, however, as he is racing off to the house he pulls the helmet off in a way which couldn't have been accomplished with the strap still fastened.
Continuity mistake: At the start of the movie, two wooden balls are created to name the next victim and killer. After the balls are created, they are dull and unpolished, but their travel through the tubes shows them to now be highly polished and shiny.