Other mistake: When Scotty goes to the holodeck to visit the original Enterprise, the computer tells him there are 5 Federation vessels with that name. (NX-01 served before the founding of the Federation so this is technically correct.) Scotty specifies NCC-1701, "no A, B, C or D." The computer then tells him the program is ready. The computer should have asked him if he wanted pre or post refit NCC-1701. The ship we see in the Original Series was rebuilt/refit into the ship we see in The Motion Picture.
Other mistake: In the transporter room, Data asks the computer what file log is shown. The computer reply is "Transport Log 759", Data confirms "That is the correct log", but the screen reads "Transport Log 721".
Other mistake: As the cloaked Warbird looks at the Enterprise, the registry number on the under side of the saucer is reversed.
Other mistake: As Beverly points to a planet on the monitor, the read out on the planet is upside down.
Chosen answer: The uniform does indeed change colour. It may be due to the need for a green screen in part, or perhaps some lighting altering our perception. That being said, it certainly looks green at the start, blue thereafter.
The show has been done in HD now and not sure if they fix this problem.
Dan23