Plot hole: Anderton's wife gains entry into the jailhouse using her husband's eyeball - but he's already locked up inside, so his eye would not still have access to enter as it pleased. Any place anywhere that would have any sort of security system requiring anything from a simple passcode to a card key to a retinal scan, would immediately delete the user in such instances from all rights. And would also certainly report on any attempted use of such (retinal scan, pass code, whatever). (02:00:45)
Plot hole: Anderton getting to Crow pivoted on seeing the Precog visions of Anderton killing Crow. But it's a causal loop. How did it happen the first time without the vision? To top it off, Anderton had Agatha in the room. Later Burgess points our to Witwer that there are no signs of Precrime descending on him because the Precogs can't see him about to kill Witwer because of their separated condition. However, that's the exact same condition the Precogs were in when Anderton was supposed to shoot Crow...so how would it be seen in pre-vision?
Continuity mistake: When the cheated husband says "I forgot my glasses", the lover is on top of the wife, and tries to sneak by bouncing way up and then turning to his left. The jump is cut and the angle changes to a close up of the lover, but this time he is right next to the wife, as if he had just moved aside. No bounce. You'll need to freeze the image to notice it.
Plot hole: Burgess frames Anderton for Witwer's murder, using Anderton's gun in Anderton's house, but Anderton has an airtight alibi; at the same time as the murder, he was arriving at his ex-wife's home. His ex is even on the phone with Burgess, who asks if that's John arriving with Agatha.
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. (00:01:55)
Other mistake: At the beginning of the movie, we learn that the precogs "do not see what you intend to do, only what you will do" and that they cannot see suicides. At the end, Burgess intends to kill Anderton but does not go through with it; he commits suicide instead. Given these two facts, the precogs should not have seen Burgess' confrontation with Anderton at the end, and a red ball should not have been created.
Plot hole: In the scene where Anderton is talking with Hineman, she says to him that "You will bring down the [Precrime] system yourself if you manage to kill your victim. That would be the most spectacular public display of how Precrime didn't work." Shouldn't she be saying "If you manage to not kill your victim"? (01:01:30)