Visible crew/equipment: When Anderton visits his wife after the auto plant scene, the camera pans around the car and the camera operator is clearly seen in the reflection on the bumper. (01:57:05)
Visible crew/equipment: When Lamar shoots Witwer it shows the the bullet's point of entry. Looking closely at his shirt, you can see the outline of the square/rectangular blood pack. (01:48:50)
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)
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.
Visible crew/equipment: After the scene in the car factory when Anderton drives up to Hineman's place, he parks his car and opens the door. When he opens the door, you can very easily see a cameraman bent down reflected in the car door. (00:53:10)
Visible crew/equipment: When John Anderton shoots Leo Crow, the camera mounted on a crane can be seen reflected on the building's glass in the outside shot just a second before the man defenestrates himself.
Visible crew/equipment: When Anderton is about to enter the Lexus factory he runs into the cops' car. When the passenger door opens, you can see the reflection of a crewmember. (00:49:35)
Visible crew/equipment: When John Anderton is walking around the hotel room before meeting Leo Crow, just before he spots the photos on the bed, he glances over towards the direction of the bed - if you look to the left of him, you can make out a cameraman's face and hand where he is holding a camera in the reflection of the glass window.
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