Continuity mistake: When Anderton is mad about the doctor sticking him with the anesthesia and is holding him on the counter holding the doctor's arm behind him, the needle changes places quickly and ends up in different places. (01:03:20)
Continuity mistake: When Anderton first starts getting chased, he kicks the glass out of the back side of the automated car. He then proceeds to climb on the top of it at which point the car then goes over a cliff leaving Anderton hanging from it. He then climbs onto the back side of the car (as this is not the top) and the glass is present again.
Other mistake: The name on the red ball at the beginning has the name 'Donald Dubin' on it. But in the end credits, it is spelled 'Donald Doobin'. (00:02:10 - 02:17:40)
Visible crew/equipment: In the scene where Anderton is going to kill Crow, the camera angle changes to behind Crow. In the window behind him you can see the demolitions charge used to create a bullet hole and crack the glass. (01:44:05)
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?
Other mistake: When Anderton and the pre-cops are gearing up to prevent the Howard Marks murder, there is a shot of Anderton loading his gun. If you watch closely you can see he places a clip under the gun but doesn't actually put it in, he just sort of mimes inserting it. (00:08:55)
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. (00:11:00)
Continuity mistake: When the pre crime cops are looking for John in the mall, there are 7 of them on the upper balcony, the leader tells two of them to "take the east end," and you see two of them run off to the left, yet in the following shot all seven of them are running to the right. (01:33:15)
Factual error: In the scene when Anderton escapes out of the Maglev Car, there's barely any wind blowing his hair or jacket, even though the car is moving at intense speeds and he can barely keep his balance. He jumps from car to car on a vertical track, jacket is not moving. Then he jumps on to the roof of another car and you him from the inside of the car, there's no wind movement on him at all. (00:43:55 - 00:44:55)
Visible crew/equipment: When John and Agatha come to Rufus T Riley's place there is a low camera view of them walking through a doorway as Rufus starts saying about Anderton getting 'a little jerky for himself'. To the left of the doorway the crew are reflected going backwards filming the action.
Continuity mistake: During the scene where the police first go to arrest Howard and John is deciding which door is the right one his plastic face plate is down and in the next shot it is clearly up. (00:10:55)
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.