Prot's signature sunglasses are actually a favorite pair owned and worn by U2's front man, Bono. The glasses are Brand DITA and style is discontinued. Kevin Spacey asked to borrow them for the film, which Bono agreed to under the condition that they were well cared for and were returned immediately upon completion of the film.
(at around 18 min) Kevin Spacey had to record the scene where Prot eats a whole banana (skin and all) 27 times.
The original plan was that Will Smith was to play Prot and Kevin Spacey Dr. Mark Powell. When Smith pulled out of the role, Spacey decided to play Prot.
In the novel, one of Prot's favorite movies is Starman: O Homem das Estrelas (1984), which starred Jeff Bridges, who played the title role as the alien.
Prot's departure for his home system, which is "near the constellation Lyra", is scheduled for 5:51 a.m., July 27th. On that day in New York City the sun rises at 5:48, while Lyra itself is beginning to set in the west (and eventually before sunrise as the year wears on). This implies that Prot must "grab" an Earth-skimming beam of sunlight while he still has a clear line-of-sight to K-Pax, in a rapidly narrowing window of opportunity.