Other mistake: On board the USS Reliant as it orbits Ceti Alpha 6 the systems panels show ship diagnostic diagrams including a wire model of a Constitution class hull, something the Reliant doesn't have. (00:13:01)
Other mistake: When Captain Terrell shoots himself with the phaser, the phaser disintegrates along with his body, when it should have just dropped to the ground (as often shown in the various Trek TV shows). It wouldn't make sense to explain that the phaser disintegrated because Terrell was touching it, because then it would be impossible to explain why nothing happens to the ground that people are standing on when they get shot (Director's Cut). (01:11:20)
Other mistake: After the Enterprise blows the port nacelle off the Reliant, the destroyed Reliant bridge is shown. The three sheaves of wires hanging from the ceiling should be on a tilt with the angle of the ship rather than straight down. Even accounting for the artificial gravity unit, which could have been damaged.