Corrected entry: At the beginning of the movie, the Excelsior is hit by a shockwave coming from the Klingon moon Praxis (the Excelsior would be in Federation space, dozens of light years from the moon). The force of the shockwave is such that the ship is physically thrown about, as are the crew. A blast that is so strong at such an extreme range would surely destroy not only the moon but also the Klingon homeworld and most other things in Klingon territory. This, however, isn't the case; Praxis is later shown to be only half destroyed.
Corrected entry: Captain Kirk and Dr. Mccoy escape from the Dilithium mines together with the shape shifter. They go to the surface and get out of the magnetic shield that prevents Enterprise from beaming them up. When they fight and get discovered later, it seems it is all a setup and they are beamed up by Enterprise just before they are shot. But why did the shapeshifter lead them to a place outside the magnetic field? If only they were inside it (no markings around to show they are outside the field), they could never have been saved.
Corrected entry: When Spock mind melds with Valeris, you hear a heartbeat. Whose heartbeat is this? It is specifically stated in the original series that Vulcan hearts beat almost twice as fast as humans. It is, however, never established that Vulcan metabolic functions slow during a mind meld, due to conscious physical control or otherwise.
Corrected entry: The character of Valeris was originally slated to be Lt. Saavik. The filmmakers tried to get Kirstie Alley back, but found out that her stardom in "Cheers" now made her too expensive. It was then decided that Saavik as she was known would never betray the Federation, so Valeris was created. This explains Valeris' infatuation with whether Spock is lying, as her words were originally Saavik's, mirrored in "The Wrath of Khan" (when Spock tells her, "I exaggerated," after she accuses him, "You lied.").