In The Man Trap (1966), Spock says that the planet Vulcan has no moon. But while Spock is meditating on Vulcan in this film, two moons can be seen.
Spock's first scene shows him squinting into bright sunshine - preceded by a reverse shot showing a dark sky.
Spock damages his console pretty badly when he bashes the V'ger probe's "hand". A few minutes later, the console is undamaged.
Early in the movie the crew is concerned about using warp drive while inside the solar system. At the end of the movie, Kirk gives an order to go to Warp 1 while the Enterprise is in Earth orbit.
In several shots of the Enterprise throughout, we plainly see a pair of phaser turrets just below "U.S.S. Enterprise" on top of the saucer section. As Kirk, Spock, McCoy, Decker and Ilia emerge from the saucer section en route to their V'ger encounter, the phaser turrets are completely missing. Not only this, the slope of the hull is far too steep.
When flying past Jupiter, three consecutive shots of Jupiter and its moons are shown. The first and third are from the POV of the ship as it approaches and passes Jupiter, and show the sunshine on planet and several moons coming from the port aft. The second shot shows the opposite angle of the oncoming ship, and the sunshine on the planet and 4 moons is coming from a different direction on each body, none of them from the port aft.
When Kirk rescues Spock during the spacewalk outside of the entrance to V'ger, an unconscious Spock is floating towards Kirk who catches him. They remain stationary thereafter. This would not happen in the depicted environment. With nothing to keep Kirk in place, they should both move away, at reduced speed based on their relative masses, after Kirk catches Spock.
When the USS Enterprise is seen leaving spacedock bound for V'ger, the Earth is shown in the background as the sun slowly rises behind it. Since this appears to be a stationary camera facing towards the ship, it should not be possible that the sun can be seen 'rising up at dawn' from this position in outer space. Only an observer on Earth or a camera leaving Earth's gravity would see this view of the sunrise.
When Kirk first comes on board Enterprise he is called "Admiral," and then "Captain" a few seconds later. However, it is customary for the person in command of a ship to be addressed as "Captain," regardless of his military rank.
After V'ger destroys the Klingon ships, comm station Epsilon IX continues to receive a view of V'ger. This is because there are "sensor drones" placed throughout Federation space and bordering territories throughout the galaxy. It is the same reason the Enterprise continues to receive an image of the V'ger cloud after Epsilon IX is destroyed by V'ger. It is well-known in the Star Trek universe that these drones are utilized to help transmit images back to Starfleet, if and when starships are unable to transmit the images on their own. The Enterprise attempts to use said drones to transmit images of the V'ger cloud back to Starfleet while inside the cloud. If the viewer pays attention to the dialogue in this film, they will hear at least two instances where the drones (and their functional purposes) are mentioned.
When Spock is greeted by Dr. McCoy for the first time in years, he reacts with visible revulsion and does not reply. Beneath the rivalry between Spock and McCoy, there was mutual respect and even admiration for one another. Even if Spock had since changed his mind about McCoy, he would never have treated a fellow officer and former comrade in so many adventures in such a discourteous manner. However, Spock's unusual behavior in this instance is due to the after-effects of his failed attempt to achieve Kolinahr, the total suppression of all emotion.
When Spock is doing his EVA into the interior of V'ger, the reflection we see in the visor of his spacesuit helmet should be the reverse of the image we see when looking over his shoulder, yet they are the same.
When the V'ger probe first comes onto the bridge, the portion of the set around the probe appears to "shrink". For example, the view screen is not as wide in one shot, and the dome in the bridge ceiling disappears and reappears as the probe passes in front of the helm and navigation console. This was due to a distortion effect, done to "hide" the electrician holding the light source used in this sequence. (Fixed in the 2001 Director's Edition.)
When V'ger's energy probe is on the Enterprise's bridge, there is a mismatch between the sides of the screen on each side of the probe e.g. the handrail near view screen does not match up - the left hand side of the rail is higher than the right hand side.
When Spock's shuttle is seen docking with the Enterprise from the observation deck, the star field moves in front of, rather than behind, the warp nacelles.
When Spock puts the nerve pinch on the man in charge of the suit lockers, the thruster suits in the lockers are those intended to be worn for the original Memory Wall sequence that would have followed this scene originally. The suits worn by Spock and Captain Kirk later on in the movie are of a very different design and have a larger helmet.
Just before Kirk enters Engineering, a voiceover incorrectly announces "Engineering, show me your readings on photon capacitators" instead of capacitors, which is correctly displayed in the subtitles.
When the Enterprise reaches Warp 7, the screen shows the "coming out of warp" effect. The Enterprise is actually remaining in warp, and should not show the "coming out of warp" effect until they slow down when they get to the vicinity of V'ger.
When the ship is leaving space dock, multiple, large dirt marks are present on the camera lens.
When the Enterprise moves out of the spacedock, the bracing used to hold the model can be seen silhouetted against the spacedock on the Starboard side of the ship.
As Kirk exits the shuttle at Starfleet Headquarters, immediately before he first sees Commander Sonak, a male crew member with regular 20th-century clothes is very quickly visible near the back of the shuttle next to a blonde female extra before both are obscured by Sonak's entry doorway.
Kirk's spacesuit when he makes the EVA to rescue Spock.
In the message from Epsilon 9, it is stated that the V'ger cloud measures 82 AU in diameter. 1 AU (astronomical unit) is the distance between the Earth and the sun (approx 93 million miles), so a cloud measuring 82 times this would completely cover the solar system.