The scene when Tim Allen is in a men's room overhearing how the cast of Galaxy Quest are nobodies and all the co-stars can't stand him mirrors an actual event in William Shatner's life. He discovered the exact same things about himself when he attended a 1986 convention.
Tim Allen admitted that he was quite star-struck when he met Sigourney Weaver, as he's a huge fan of Alien (1979). Allen even got Weaver to sign some of his Alien memorabilia between takes. She ultimately did, writing "Stolen by Tim Allen; Love, Sigourney Weaver", which she said made him very upset.
The casting director loved Enrico Colantoni's audition so much, she broke protocol and showed this to other actors to demonstrate how the Thermians should behave.
This film was one of the earliest to have its own domain name and website, GalaxyQuest.com (now available only via Wayback archive). However, rather than being a polished part of the film's marketing campaign, the site (in keeping with the film's fan theme) was deliberately designed to look like a fan page, with screen captures and poor HTML coding.
Although Alan Rickman hated sci-fi as a genre, he could not resist taking part in this film as he found the material very funny.