Edna Glover's scene as the Vulcan Kholinahr Master was filmed with her speaking English. Only later were Vulcan words (invented by James Doohan) recorded over the original dialogue. The phonetics of the Vulcan words were chosen to closely follow the original English script so that her lips would seem to move correctly, and English subtitles were inserted with the phrasing reworded so the change would not be obvious. For example, when the subtitles say "Our ancestors cast out their animal passions on these very sands" her lips are clearly saying "Spock, on these sands our ancestors cast out their animal passions." Other examples are "Your thoughts... give them to me" [subtitle] versus "Spock... give me your thoughts" [actual] and "Your human blood is touched by it, Spock" [subtitle] versus "It stirs your human half, Spock" [actual].
When the Vulcan Master (Edna Glover) performs a mind meld with Spock during his Kolinahr ceremony, her face drops with obvious disappointment when she learns of the space consciousness calling Spock which is clearly an emotion a Vulcan Master shouldn't be feeling. She also beams with obvious pride earlier while talking about Kolinahr as "total logic".
In the original version, Spock's first scene shows him squinting into bright sunshine - preceded by a reverse shot showing a dark sky. This error is corrected in the Director's Edition, with a new landscape and sky on Vulcan.
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. (this is fixed on the Director's Edition DVD).
As Spock arrives on the Enterprise, he's met by Checkov and a security officer, and Spock immediately walks off, leaving Checkov behind. As he arrives on the bridge, Checkov is already there, ahead of him.
AS we look through the window of the Floating Office Complex from the outside, there is no Travel Pod docked in the dock (next to the window). Moments later, after Admiral Kirk beams aboard, he and Scotty enter a Travel Pod docked at that dock. (This is corrected in The Director's Edition.)
As the bridge crew is watching the orifice beginning to open from the view screen, a quick cut from behind the Enterprise shows the orifice still completely closed. Most evident from bright light emanating beyond the opening in the bridge scene.
In the Original Star Trek Series, Spock says that the planet Vulcan has no Moon. But while Spock is meditating on Vulcan in this film, a Moon can be seen. (1979 Version and "Special Longer Version" only.) This has been fixed in the "Director's Edition," with an actual atmosphere and sky on Vulcan, eliminating the moon altogether.
When the transport shuttle arrives to deliver Spock, it's shown arriving along the starboard side of the Enterprise. As the personnel carrier docks, the shuttle piece is now shown directly aft of the Enterprise.
When Spock ejects his thruster pack during the space walk, the initial shot from behind shows it rotating counterclockwise and moving to Spock's right. There is an immediate cut to a shot from in front of Spock, and the thruster pack can be seen in the background to Spock's right (POV left), rotating counterclockwise from this angle as well.
When the Ilia-probe first breaks through the sickbay door, the top part comes undone from the frame. In the next shot of Ilia, the top of the door is back attached to the frame and the hole in the door is lower than it used to be.
As the travel pod flies by to dock with Enterprise, it is shown passing in front of a light beam that was pointing at the Enterprise's warp drive section. When the travel pod passes in front of the beam, it is lighted. However, there should have been a shadow on the Enterprise when the transporter passed by.
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 (the extra begins her own walk-through in the background once Kirk and Sonak begin speaking).
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. This has been corrected in the Director's Edition.
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 Enterprise is departing from Earth the Sun is seen to rise above the Earth. However sunrise is normally due to the rotation of the Earth, or in the case of the International Space Station the vehicle moving in a posigrade orbit round the Earth. In this case, the Enterprise is moving in the opposite direction, so if we were following it then the Sun would be seen to set if the Enterprise was in orbit. On the other hand, if the Enterprise was moving in an almost straight line, the Sun could come into view as the apparent size of the Earth diminished due to the Enterprise moving away from it. As the size of the Earth does not appear to change, the Sun can only appear to rise if the position of our viewpoint is moving in that same direction, but if that were so, we would be moving upwards, away from the Enterprise. This isn't happening either, so the scene might look nice but it is incorrect.
Incorrectly regarded as goofs: The distance between earth and the sun is 1 AU in the message from Epsilon 9 it is stated that the cloud is 82 AU, so it would completely cover the solar system: it turned off its cloud defense shield and was only about 200 miles long.
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.
Incorrectly regarded as goofs: The distance between earth and the sun is 1 AU. In the message from Epsilon 9, it is stated that the cloud is 82 AU, so it would completely cover the solar system: as it approached Earth, it turned off its cloud defense shield, and was only about 200 miles long.
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.
V'ger is 3 days away from Earth so V'ger would need to traveling many, many times the speed of light to make it from the Klingon empire to Earth in 3 days. V'ger would need to be sub-light in order for the Klingons to engage in battle, fire torpedoes at V'ger (and vice-versa), and make evasive maneuvers. It is very possible V'ger detected the Klingons and slowed to sub-light to scan them and send the high frequency message (same that they sent to the Enterprise). But of course the Klingons did not notice they were contacted and obviously taken for hostile especially when they fired their torpedoes. Same thing for the Epsilon 9 encounter.
Immediately before Spock walks out of the shuttle onto the Enterprise, there is an announcement which states; "Identity: Starfleet, inactive". Yet when on the Bridge, Spock tells Kirk that he has been monitoring their communications with Starfleet and is aware of their warp drive problems. Surely communications between the Enterprise and Starfleet would be secured, especially during a major mission, and no person who did not have a current active position in Starfleet should be able to listen in.
V'ger turns out to be "Voyager 6" because the "oya" and "6" are covered in dirt. V'ger would not know this and its memory would still be programmed to call itself "voyager". It would be like if a the label of a computer, say, let's say "Dell" had the "D" covered up, the boot-up screen would not read, "ell" during post, it would still read, "Dell"
Near the beginning of the movie Kirk tells Scotty "...an alien object of unbelievable destructive power is less than three days away from this planet (Earth). The only starship interception range is the Enterprise." While this is of course important for the whole plot of the movie and the reason why the Enterprise should intercept V'ger, it is highly unlikely that in generally and also especially in a time with war conditions with for example the Klingon Empire there is no protective fleet (not one ship apparently) inside the Solar System or within a 3-days-journey of it.
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 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.
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.
When the USS Enterprise is seen leaving spacedock bound for Vger, 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 earths gravity would see this view of the sunrise.
In several shots of the Enterprise, travel pods and various other exterior shots, there are lights on surfaces that have no apparent light source being shone upon impossible angles to be lit from a source from the object.
The goof items below may give away important plot points.
Incorrectly regarded as goofs
Even if it is assumed that the advanced machine race named the probe "V'Ger" based on the letters on its nameplate, there is no explanation as to why they would understand the English alphabet, or how the letters were pronounced. However, the real life Voyager 1 and Voyager 2 probes both had the "golden record." This was a phonograph record attached to the probes with images and spoken words on it. Since Voyager 6 was made the same as the real life Voyagers, it's very likely Voyager 6 has a golden record as well. Any advanced civilization would have been able to learn the English language and proper pronunciation from the golden record.
The entire twist of the plot centers around "V-Ger" actually being "Voyager," as demonstrated by the corroded name plate on the Voyager probe. We are left to assume that nowhere in its programming (or anywhere else) did Voyager have its name recorded and that the advanced computer race was unable to scrape off the carbon scoring on the name plate.