Trivia: At the beginning of the movie Kirk rescues McCoy from a jail of some sort. Before leaving Kirk asks McCoy how many fingers he's holding up and does the Vulcan hand thing. However, Shatner had severe difficulties putting his fingers into place, they just wouldn't hold into position. So the crew wound up wrapping fishing line around Shatner's fingers, he would put them into position out of the camera and the shot quickly jumped while his fingers where still in place. If you look closely you see the line around his fingers. (Note that this problem occurred several times during Star Trek, actually, Nimoy and Leonard seem to be the only people doing this without a problem.)
Trivia: While it's well-known the voice of HAL in "2001: A Space Odyssey" is Canadian actor Douglas Rain, who returned to reprise his role in this film, it's less known that the voice of SAL is credited to "Olga Mallsnerd" which is a false name used by none other than Candice Bergen. (00:14:05)
Trivia: In the final scene, when Winston and Julia are playing chess, Winston uses a tactic of going around and hitting from behind. Only minutes later, the news report that Oceanarian forcer defeated Eurasian forces in Africa by using the same tactic. Nothing major but it makes a good point about the rate of citizen monitoring and news manipulation in Oceanaria.
Trivia: When director Jeff Kanew was interviewed by the producers, they asked what kind of movie he thought he could make given the material. He responded, "One I would be embarrassed to have my name on." They hired him immediately.