Revealing mistake: When the shuttle pod makes its first pass on the port side of the space dock (starboard of the shuttle) a piece of the earth shows over the last strut as the pod passes (blu-ray and Netflix version).
Continuity mistake: After Ilia is abducted by the V'Ger plasma energy beam on the bridge, her tricorder falls on the chair. The chair is facing a different angle than it was before. Also, you can see the white tips of a pair of shoes from someone standing next to the chair on the left. Presumably, this is supposed to be Kirk, but he is too far away to see his feet in that shot.
Continuity mistake: As the camera goes in on the window of the station, there is no travel pod parked at the airlock. When Kirk and Scotty go to leave, there is one conveniently there, with no announcement of arrival. (Corrected in the Director's Edition).
Revealing mistake: As they prepare for Warp speed the man is touching control buttons on the console in Engineering. If you look closely, as he touches them, the entire panel reacts to his touches, suggesting that all the lighted buttons and the surface are all one piece.
Other mistake: When Kirk and Scotty are in the travel pod going to the Enterprise, one shot of the outside of the pod has them looking like two dimensional cut outs. Also, from interior to exterior shots of the pod Kirk goes from facing directly ahead, to a quarter profile and back.
Continuity mistake: When the Enterprise first leaves space dock, the deflector array is orange until warp speed, then it's blue. Inside V'Ger, it alternates from orange to blue.
Answer: Deltans exude an intensely potent and effective chemical substance known as pheromones, which act as signals arousing an intense sexual reaction in other species (in other ST material it's inferred that its potency is so extreme that a non-Deltan risks insanity in a sexual encounter with a Deltan). Upon entering Starfleet, Deltans must swear "an oath of celibacy" so as not to influence or take advantage of crewmembers. That is why Lt. Ilia stated that her "oath of celibacy" was on record.
Super Grover