When the crew is pulling up the grates to lower the photon torpedo into its launch track, you can see a crewman in a red jacket in the background. The way he is fidgeting, he is obviously an extra that didn't know what to do after "Action" was yelled. Though, I guess we could be charitable and say he was a green ensign unsure of what to do at Red Alert.
This film was supposed to be called "The Vengeance of Khan". They changed the title because of the rumor that "Return of the Jedi" was going to be called "Revenge of the Jedi" and released the following year.
This movie is basically a retelling of another story. When the camera first pans the shelves of the Botany Bay it stops and centers on one book on the shelf in particular.....Moby Dick. That is what this movie is about. Khan is Ahab, The Enterprise is Moby Dick. At one point in the book the whale is circling Ahab's ship on the ocean. At one point in the movie the Enterprise is circling the Reliant (Khan's ship) in the Motara Nebula. Ahab had a scar up one entire side of his body given to him by an encounter with the Whale. At the end of the movie Khan has a burn mark/scar up one side of his body as well. Not to mention that Khan quotes from Moby Dick throughout the movie. The last quote he utters is one that Ahab uttered "From Hell's heart, I stab at thee, for hate's sake I spit my last breath at thee."
Kirstie Alley once forgot to remove her Vulcan ears before going on a date after filming.
Kirk and Khan both mention that Khan was marooned on Ceti Alpha V fifteen years earlier. This movie was released fifteen years after "Space Seed" aired on television.
On the original movie poster and certain DVD releases, it shows the Enterprise firing on Space Station Regula One, when no such scene exists in the movie.
The death of Spock was leaked out very early on in the production of this show (they suspected Roddenberry as he was very against it). When they were planning the training scenario at the beginning of the movie, it was originally going to be about halfway through the movie. They decided, however, to move it to the beginning so we would assume it was real. They then decided to 'kill' Spock off right there at the beginning (along with the rest of the bridge crew). That way, those watching the show for the first time who were told that Spock would die, would assume (after it was revealed that the beginning was a training scenario) that Spock was only going to pretend to die. That way, even though they were told that Spock died in the movie, they were still surprised when he actually did.
Kirk and Khan never meet face to face during the movie. They only speak to each other over communication links such as starship view screens. They did meet in the original TV series episode.
Prop master Joe Longo, a Ricardo Montalban and Fantasy Island fan, modified a small toy robot, painted a tux on it and used a poster to give it Tattoo's face. When Montalban first pulled into the studio parking lot, Longo sent the mechanical Tattoo toddling out to his car. Every day of the production after that, "Tattoo" arrived in the passenger seat of Montalban's car, came to the set with him, and went home every night to play around the actor's swimming pool.