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: The voice on the flight recorder is that of the film's producer, Harve Bennett.
Trivia: The first time we hear of "transwarp drive" technology is in The Search for Spock; presumably, using Transwarp Drive, the Excelsior should be able to easily overtake the Enterprise, even at maximum warp. Montgomery Scott easily sabotages the Excelsior, however, and we never see the transwarp drive in action. For some reason not explained in Star Trek canon, the Great Transwarp Experiment was abandoned as a failure at this point, so we never learn of the actual maximum speed of a starship with Transwarp Drive.
Trivia: Spock's coffin is a photon torpedo capsule with "Mark VI" written on the top. Mark VI is the chapter in the Bible which relates the raising of John the Baptist from the dead.