Executive Meddling (According to Meyer, lawyers decided who got credited, and paid, for the screenplay. "I just wrote it and they put somebody's name on it.") As for the whole story The full story- before Nick Meyer was hired as director, there had been five different previous drafts of the script (four written by Jack B Sowards, one by Samuel Peeples) — all with considerably different plots and all unsatisfactory. The special effects company needed to have a proper screenplay for the film within twelve days or the movie basically wouldn't happen, so Meyer volunteered to write a definitive screenplay within twelve days which would combine all the best aspects of the previous drafts. Upon being told they wouldn't even be able to organize a screenwriter's credit for him in twelve days, Meyer decided to do it anyway and try to organize a deal later. In the end he actually did complete the screenplay within twelve days but ended up going uncredited and unpaid for it, with Sowards getting the sole credit.
Judson Scott (Joachim) doesn't appear at all in the credits, due to an overzealous agent trying to get him star billing without his knowledge.
Misaimed Fandom: In-universe. Moby-Dick is part of Khan's private library and he quotes Captain Ahab throughout the movie. Either Khan missed the point of the novel or alternatively, he understood the point of the novel completely and recognized the parallels between himself and Ahab, but was so consumed by his rage that he didn't care, or just so arrogant that he believed that, unlike Ahab, he could slay his white whale without destroying himself and his crew. Also, it's possible that Khan knew he would die as a result of his actions, but he wanted to take Kirk with him. A "The Only One Allowed to Defeat You"-sort of thing.
No Budget: Not completely, but given the cost overruns on Star Trek The Motion Picture, they definitely had to save money wherever they could. As a result, all of the Enterprise shots in drydock (and the "beauty shot" after its launch) were recycled from the first movie. Several uniforms were reused as well - the thruster suits, engineering suits, and McCoy's medical shirt were reused straight-up with only minor tweaks, and the one-piece jumpsuit uniforms were dyed and tweaked into the cadet/noncom jumpsuits. Even Spock's black robe is from the first movie.
Promoted Fangirl: Kirstie Alley was a big-time fan of the original series who was extremely excited to be able to play a role alongside Leonard Nimoy. Apparently, she was quite apt at the Vulcan characterization which helped to land her the role.
Prop Recycling: A time-honored Star Trek tradition. In particular, the Enterprise and Reliant bridge sets are in fact the same set. It was designed modularly so that the different sections could be switched around to present a different layout.
The Reliant studio model is built largely from spare Enterprise model parts with a few additions and one major notable subtraction (The secondary hull is removed entirely with the nacelles grafted directly onto the saucer section)
Pointedly shown with a background shot: when Chekov and Terrell are arguing about Carol Marcus's reaction about "transplanting" the life forms from Ceti Alpha VI, Checkov is standing beside a monitor showing the lower hull of the Enterprise.
Throw It In: Harve Bennett accidentally saw the Reliant designs upside down, and the crew made the models to fit that.
What Could Have Been: Spock'sHeroic Sacrifice was originally placed at the middle of the movie, in an attempt to mimic the Psycho gambit. When they wisely decided to make it the emotional climax of the film instead, Peter Preston's sacrifice was put in its place instead. Similarly, the whole ordeal was practically spoiled before the movie began filming because it was what lured him back to the franchise. The Kobayashi Maru sequence was intended as a way to throw off expectations.
To elaborate: An early version of the script got leaked, including the fact that Spock died. Afterwards, the Kobayashi Maru sequence, which included Spock fake-dying, was added to fake-out moviegoers and make them think that that was the "death" that had been promised.
Ricardo Montelban considered turning down reprising the role of Khan due to lack of screen time. When he realized how much of an impact Khan had (even when he's not on screen, Khan is affecting every action every character in the movie takes), he signed onto the film.
The preliminary design◊ for the U.S.S. Reliant was initially much different than what was eventually seen in the film, with the "roll-bar" torpedo bay missing and the warp nacelles above the dish, like on the Enterprise. However, when Harve Bennett received the design for approval, he viewed the drawing upside-down and assumed that was Reliant's intended look. The production team debated whether or not to send the drawing back to Bennett right-side-up, but he was shooting in Israel by then and there was little time to contact him. They added the roll bar and repositioned the nacelles, resulting in the Reliant we are familiar with.
Even before that stage: they originally considered having the Reliant be another "Constitution"-class starship (it was the only class of Federation ship seen on Trek before that time), but then realized the audience would have trouble telling it apart from the Enterprise during the battle sequences. Thus it was decided to make Reliant part of the "Miranda"-class.
Spock's death was originally intended to be permanent, as Nimoy had grown tired of the franchise and even almost didn't come back for the first film. However, working on this film was such a good experience he decided to stay with it.