Continuity mistake: In the final scene on the bridge, Spock and McCoy are wearing colored arm bands which identify their departments: Spock's is orange (for Science) and McCoy's is green (for Medical). In the very last shot, Spock is wearing the green band and McCoy is wearing the orange one.
Continuity mistake: (ABC Television version only) When Kirk leaves the Enterprise, you can see the set behind him. Kirk's suit also changes from the time that he is seen leaving the ship to the time that Spock is sent back unconscious. Unfinished scenes were added before being aired on television.
Continuity mistake: In the 2000 Director's Edition only: during the scene in which Kirk and McCoy are asking Spock why he has returned to the Enterprise, they added an effects shot of the Enterprise's warp nacelle outside the window. Keep an eye on it throughout the scene. Even considering the fact that the camera angle changes throughout the scene, the nacelle appears to "move around" (side-to-side, up-and-down, nearer/closer to the window) and the perspective/foreshortening of it never changes in relation to the camera angle.
Continuity mistake: After Spock's arrival, the Enterprise is finally able to exceed Warp 1. At the end of the test run, the shot shows the Enterprise, the beautiful light spectrum tube, and the pop/explosion created by warp speed. The problem is the pop/explosion and the spectrum tube do not line up. It's almost as if the two started at different points.
Continuity mistake: Near the end of the movie, Kirk reads the nameplate & begins to wipe off the "V-GER" sign, he uses his bare fingers to clean the sign. As he circles "V-GER" you see his hands beside them and they are perfectly clean. His hands should have shown some evidence of wiping off the VOYAGER sign.