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).
Factual error: The cloud surrounding V'ger is noted as being 82 AU (Astronomical Units) across. This is more than the distance from the Sun to Pluto and back. As such, V'ger would never have been able to approach Earth. This was adjusted to 2 AU in the special edition DVD.