In the opening credits, there is a six-second-long pause between William Shatner and DeForest Kelley's names, where Leonard Nimoy's name would normally be. It's only one second between each of the other names.
The film's villains were originally intended to be Romulans, but upper studio management wanted Klingons to be used, since they were better-known enemies. By the time the decision was made, the Romulan warship was already built, and they did not want the expense of replacing it. However, since Star Trek (1966) had already established that the Klingons and Romulans had shared technologies and ships in the past (for exactly the same real-world cost-cutting reasons), the idea of Klingons using a Romulan-style vessel was not a problem.
The U.S.S. Grissom was named after astronaut Virgil I. Gus Grissom, who was killed when the Apollo 1 spacecraft caught fire on January 27, 1967, during a launch simulation test. The fire also killed astronauts Edward H. White II and Roger B. Chaffee.
Production was endangered by the great fire at Paramount Studios. William Shatner helped fight the fire and rescue a crew member before firefighter reinforcements arrived. Shatner said that his motivation for doing so was purely to save a day on the shooting schedule, as he had to make a deadline to be available for shooting on a new season of T.J. Hooker (1982).
According to Robin Curtis in the Blu-ray making-of documentary, Christopher Lloyd didn't fully understand the use of the communicators. He would often shout his lines into the air rather than speak into the communicator. (An example she used: When he says "Bring me up" while on the Genesis Planet, he yelled at the sky as if the ship could hear him.) He had to be repeatedly told not to yell at the sky.
Grace Lee Whitney: As Janice Rand, Captain Kirk's yeoman in season one of Star Trek (1966), and who returned as transporter chief in Star Trek: The Motion Picture (1979). Appears during the Enterprise's docking sequence. She is the red haired officer in the spacedock lounge who shakes her head in disbelief, worried for her former crew, as she sees the ship's extensive damage.