i am re-watching this now on SyFy...the only thing that sticks out budget-wise that looks "bad" is the conference seen at the beginning with Spock & the Enterprise crew and Starfleet officials...while a little bit diverse as far as earthlings...no other non-human top Starfleet brass? Not even a Vulcan?
THAT seemed cheap to me...and would have been an interesting contrast to a later scene.
Later on a Klingon calls the Federation a "human only" club, which seemed to be confirmed from the lack of other Federation representation.
While there may be some plotholes or other flaws...overall, it's a good Trek MOVIE (as opposed to a long episode, like Insurrection felt like). i still like TWOK better, but this was a good one for an ending.