The "earpiece" that John Anderton uses to call Director Lamar Burgess at the climax of the film was actually a Bang & Olufsen A8 earphone with the cord cut off.
Most of the film was over lit and the negative was bleach washed to give the film it's desaturated color scheme. Exceptions are John's dream about his son and his recorded home movies.
The three Pre-Cogs are named after three famous murder mystery writers; Agatha (for Agatha Christie, creator of Hercule Poiroit), Arthur (for Sir Arthur Conan Doyle, creator of Sherlock Holmes) and Dashiell (for Dashiell Hammett, creator of Sam Spade)
Three years before starting production, Steven Spielberg put together a panel of futurists to design the futuristic technologies that would be depicted in the film.