Trivia: Paul Thomas Anderson, who directed Tom Cruise in Magnolia, has a cameo on the train. It is reported that he is so hard to find that Anderson himself does not know where he appears.
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. (00:46:10)
Trivia: The flames in the fire at the end of the film when the camera pans out of the cottage are in the shape of AI, Speilberg's previous film!
Trivia: The author has given the three pre-cogs the first names of famous crime writers: Agatha (Christie), Dashiell (Hammett) and (Sir) Arthur (Conan Doyle).
Trivia: When John takes Agatha from PreCrime, Colin Farrell asks how much time do they have before John commits his murder, he is answered "51 minutes and 28 seconds", the time remaining until the end of the movie.
Trivia: The man that is being told "You're the man!" in the club that John takes Agatha to is Scott Frank, the writer of the movie.
Trivia: On the DVD extras, the sound designer for Minority Report explains that he stuck a contact mike on his fancy new washing machine to obtain the sound samples that became the sounds made by the maglev cars. In the scene where maglev cars race down the side of a skyscraper, when Anderton is standing on one end of his maglev car, so that it is now carrying an unbalanced load, you can hear the EXACT unmodified noise of a washing machine when it has an unbalanced load. (00:44:32)
Trivia: The guy that plays the hotel clerk, the one that Anderton pulls the gun on in order to see the registration on the computer, is really Tom Cruise's cousin. He is best known for his role as the killer in "In The Bedroom".
Trivia: In the short story, Anderton was overweight, balding, and middle aged. Nothing to do with Tom Cruise.
Answer: Well, there isn't really a simple solution, but here goes. For a pre-vision to form, there have be two things present within the range of the precog ability (which appears to be limited to the Washington area - regardless of the stated plan to take the programme countrywide, there's never any indication that the precogs can sense beyond that range). Firstly, someone with the intent to kill. Secondly, there has to be a target for that intent within the range of the precogs. Anderton is present, and has the intent within him to kill the man who took his son, but has no target - the real kidnapper is presumably either dead or beyond the precog ability. Burgess, by bribing Crow to pretend to be that man, has provided a viable target for Anderton's intent within the range of the precog ability, thus triggering the prevision, and beginning the chain of events.
Tailkinker ★
The above answers the question, but there do appear to be some time travel issues with this plot point in the movie. Burgess set things up for Crow to fake being the kidnapper and thus triggering Jon's desire to kill that person, everything starts by the pre-cogs seeing the future. If the pre-cogs did not exist or did not have the vision, Jon would have never known that Leo Crow existed and would have continued on without having killed anyone. This is unique within the movie, as the other murders would have been commited regardless of whether or not the pre-cogs saw it. In this case, the ONLY reason this murder occurred is because the pre-cogs saw it.
oldbaldyone
Thinking about this a little more, it could be conceivable that Burgess had planned a different option for Jon finding Crow. We just never saw that on screen, because the precogs changed everything to an alternative future timeline once they saw the original murder. Originally, Jon could have been triggered by Burgess himself, stating that they got a lead on his son's murder and pointing him to Crow.
oldbaldyone
No I think Burgess set it up so that Anderton would find Crow because of the precogs, not have a different plan set up before or else it could be possible Burgess himself would be visible in the prevision. He manipulated the system perfectly, he has done it before after all. He knows exactly how the precogs work so he is able to set it up so that it's untraceable. Except, except for the fact there is always a choice. Only then did it go wrong for him. This proves both true for Anderton and Burgess in the end.
lionhead