Revealing mistake: The shot of the Enterprise finally clearing free of the dry-dock shows a supporting pylon protruding from the starboard side of the engineering section of the starship miniature. (Corrected in the Director's Edition).
Continuity mistake: When V'Ger first appears on the bridge as a column of light, you can see that the two sides of the image don't match up, because they tried to splice the special effects person who was moving the column out of the shot.
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. (00:53:35 - 00:56:30)
Visible crew/equipment: When the four officers and Ilia exit the ship onto the hull and begin walking towards the V-ger structure, the outline of the hole left in the matte painting of the Enterprise saucer section is visible. (Corrected in the Director's Edition).
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.
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.
Factual error: In between the scenes when they are leaving Earth and passing through the Jupiter system, you can see stars flying by on the viewer. How could they be flying by stars if they haven't even left the Solar System?
Factual error: Right before Epsilon XI gets vaporized by V'Ger, Lieutenant Commander Branch (the person talking during the transmission seen during the meeting on the Recreation Deck) states that V'Ger is 82 AU's in diameter. Something that big would not even fit in our solar system, as 82 AU's is about 2.7 times the distance Neptune is from the Sun (corrected in the Director's Edition).