(at around 38 mins) When the Leo Crow murder is first envisioned by the Precogs, Jad says that the "time of occurrence is 15:06 hours", which is 3:06pm. After Anderton sees that it's him in the prevision, he sets the alarm on his watch for 35 hours and 56 minutes. Counting backwards from 3:06pm this means that it is currently just after 3am when Anderton, Jad, Wally and the rest of PreCrime are at work. Also, when Anderton tries to escape on the MagLev and calls Lamar in his office, it is obviously in broad daylight and not 3am.
(at around 1h 40 mins) When John Anderton and Agatha approach the door of room 1006 where Crow is supposed to be staying, the doorknob is on the left side of the door. In the next shot, when John Anderton knocks on and opens the door, the doorknob is on the right side.
(at around 15 mins) In the advertisement supporting the Precog program, the narrator states that within a month of starting the program, the murder rate in Washington DC came down 90%. Later in the same ad, however, a clip is shown of Director Burgess stating that in the 6 months the Precog program has been running, there hasn't been a single murder in DC. If this was the case, the murder rate would have been down 100% after the first month, not 90%.
(at around 44 mins) When Anderton's vehicle is locked down after he has been featured in a Precog murder vision, Anderton kicks out the side window of the car and climbs out. The car then drops vertically with Anderton holding onto the side. When he climbs on top of the car (really its side), he is standing on the window which he kicked out moments before.
(at around 1h 19 mins) When the robots are looking for Anderton to scan his eye, he grabs a small cooler of ice and throws it into the bathtub to get in and hide. The next time the camera shows the tub, there is nearly 10 times as much ice in the tub.
(at around 15 mins) Signs advertise an election to be held on Tuesday, April 22, 2054. 22 April 2054 will be a Wednesday. Even if the movie occurs in late 2054 and the election will be on April 22, 2055, that's a Thursday.
(at around 1h 11 mins) When Lara goes into her "darkroom" to pull a print out of the fixer to be washed, the door is open, the light is on, and there are windows that are uncovered.
(at around 44 mins) During the escape scene from the maglev car, John struggles to climb on top of his car while the latter is almost free falling. In reality, with both John and the car falling vertically, their relative speed would be almost identical and he could have easily climbed on top of it.
(At around 15 minutes) The vote is reported to happen on Tuesday 22nd April 2054. However 22nd April 2054 will be a Wednesday.
At the start of the film, the Precogs predict a murder will take place in which Howard Marks will kill his wife Sarah Marks and her lover Donald Dubin. However, the PreCrime team have trouble pinpointing where the murder will take place as there are eight "Howard Marks" listed in the local district. But since his wife's name was given as a victim, it seems unlikely that they would have any trouble finding their address, particularly given the level of technology at their disposal and the extent to which people are "databased" in that era. However, the reason it took the PreCrime team so long to locate the address is because the Markses had just moved, and their new address was not yet known.
(at around 23 mins) While Anderton is jogging through the street, an ad for PreCrime is playing, during which a future-victim states "he was going to rape me." However, later when Witwer is asking the PreCrime crew questions they discuss how the Precogs cannot see rape because of "the nature of murder". If the attacker were only going to rape her, the Precogs would not have predicted it, but if the attacker had planned to kill her after the rape, the rape would most likely have been seen as part of the Precogs' vision. Besides, it might have been a false story, just to increase a support for the program.
(at around 1h 35 mins) When John takes Agatha to see his hacker friend they escape with the aid of Agatha's immediate future visions. However, at the start of the movie it is explained that the Precogs can only see future murders, not immediate non-murder futures. On the other hand, the Precogs might have been able to foresee minor facts from an immediate future, especially that Agatha had a gift.
On two separate occasions, an individual is held at gunpoint: When Anderton threatens the receptionist at Crow's hotel and when Lara threatens Gideon in the prison. But if there has been no murder as a result of PreCrime, neither individual should feel their life is threatened, as they would reasonably expect to be rescued if they were indeed about to be killed. However, the gun could be used to inflict pain, not to commit murder, so no one would be coming to their rescue.
(at around 22 mins) Danny Witwer is right in stating "It's not the future if you stop it. Isn't that a fundamental paradox?" Anderton replies, "Just because you prevented it from happening doesn't change the fact that it was going to happen."
If you prevent something from happening that means it was never going happen in the first place. Witwer's point was proven when he caught the rolling ball from dropping to the floor. Since Witwer stopped it it was never meant to fall. However, all possible moments have several potential futures, all of which bar one are stopped for one reason or another, often by people. Based on their experience with the laws of physics, everyone in the room knew that the most likely future of the ball was that it was going to fall, but Witwer simply stopped that one possible future and replaced it by another one, so he never prevented "the future" as such.
(at around 49 mins) In the alley where the police are attempting to subdue Anderton, he takes a sick stick and pokes one of the policemen who vomits immediately, but the vomit is coming from "below" his mouth - the "vomit tube" is mis-positioned on the left side of the actor's face.
(at around 49 mins) When Anderton is being chased through the alleyway, the hole cut in his leather jacket for his safety harness is clearly visible when he is at the top of the fire-escape.
(at around 1h 8 mins) Just before Anderton is about to undergo eye surgery, the doctor says, "She is already smitten....she only has eyes for you." In the background Tom Cruise breaks character and begins to laugh before the line is even spoken.
(at around 2h 10 mins) During the "Press Conference" Lamar Burgess walks out a multi-paneled glass door. As the camera pushes toward his face we can see the etched glass makers mark on the top left corner of one panel caused by the back lighting. When he is shown through that same panel a few shots later, that mark cannot be seen, showing it was shot through a different piece of glass.
(at around 1h 3 mins) Iris cuts her hand on a vine, then immediately opens her hand to reveal a large cut which is already bled out and scabbed over.
(at around 2h 20 mins) Joel Gretsch's character is listed as "Donald Doobin" in the credits, but the name appears in the movie as "Donald Dubin".
Agatha, who has been kept motionless in a pool of water for years, is able to get up and run, without any signs of postural hypotension or muscle wasting.
(at around 1h 16 mins) The TV at Dr. Solomon's apartment shows Anderton featured on Cops (1989). The show was canceled in 2020; which, of course, no one could have predicted in 2002.
(at around 47 mins) Woman entering the train after Anderton is being positively eye-scanned with closed eyes and seconds after that rises her view at the scanner to be scanned. There are suggestions that eye-scanning does not work with closed eyes, as the spider robots need to see persons eyes opened.
(at around 1h 8 mins) When Anderton remembers Solomon P. Eddie set his patients on fire, Eddie says "I put 'em out!" and then "Some not as quickly as others..." but his mouth does not match the words.
(at around 1h 9 mins) Dr. Solomon Eddie speaks of his days in prison. His statement beginning "For true enlightenment...", and you hear, "...a large fellow with an attitude...". However his lips say, "a large fellow with a hard on".
After John's chase in the Lexus, a crouching crewmember in a white shirt is reflected in the car door as it opens.
(at around 38 mins) If red balls are a murder of passion which give them less time to find the murder than brown balls which are premeditated and can have a lead time of days then Anderton's ball should have been red. His ball came out brown as premeditated but he didn't even know the man he was going to kill until a few minutes before it was supposed to happen.
An idea, that the Precogs knew names of victims and murderers is difficult to justify, since they could only foresee images of what was going to happen.
(at around 13 mins) When Anderton is arresting Howard Marks, he states the date as April 22. Later while Anderton is running, the commercial states the vote on the National Precog Initiative is on April 22 and later that same day while he is walking with Burgess (at around 21 mins), Lamar says that "in one week" the people will vote on the initiative.
(at around 28 mins) No detectives or other police officers are ever allowed into the Precog temple in order to prevent tampering, yet after Witwer and the other detectives leave, Wally (the Precog caretaker) walks out of the room leaving Anderton alone with the Precogs.
(at around 1h 3 mins) In conversation with John Anderton, Dr. Iris Hineman said: "It's always in the more gifted of the three." One uses the term "more" when comparing two items. To compare three or more, the correct term is "most".
(at around 1h 40 mins) When Anderton is in Crow's building he says that he must find out about the situation - if he had just waited 10 more minutes, the vision would have been proved false.
(at around 1h 35 mins) When Agatha and Anderton enter the apartment building and are looking for Leo's Room # at the front desk area, after Anderton says "he's here", Agatha clearly says "Anderson, leave"... instead of calling him "Anderton".