(at around 1h 2 mins) The scene where Lois Smith (Dr Iris Hineman) kisses Tom Cruise was not scripted. Cruise's reaction is of genuine surprise.
The "Precogs" were all named after famous mystery writers: Dashiell Hammett, Sir Arthur Conan Doyle, and Dame Agatha Christie.
(at around 1h 21 mins) For the scene where Anderton holds his breath in the bathtub, Steven Spielberg was going to create the air bubble rising with CGI, but Tom Cruise took the time and learned how to do it himself.
Tom Cruise and Steven Spielberg both agreed to waive their usual salary to help keep the film's budget under $100 million. They agreed to take 15% of the film's gross instead.
Cinematographer Janusz Kaminski did a bleach bypass on the film, effectively skipping the bleaching of the silver halide crystals in the film in order to create the desaturated silver tinted colors.
Cameron Crowe: (at around 47 mins) Tom Cruise's director from Jerry Maguire: A Grande Virada (1996) and Vanilla Sky (2001) appears as a commuter on the train who looks at Anderton over the top of his newspaper and recognizes him. In the same shot, the blonde woman sitting behind him is Cameron Diaz.
Paul Thomas Anderson: (at around 47 mins) Tom Cruise's director in Magnólia (1999) as a man on the train. It is reported that he is so hard to find that Anderson himself does not know where he appears.
Scott Frank: (at around 1h 35 mins) The co-writer appears as a customer in the cyber parlor, the one who receives an award and is being congratulated ("You're the man").