People criticize this movie a lot because it's really slow, has a weak plot, and the characters really weren't themselves. I don't disagree with these criticisms, but there are elements of the movie that really deserve a lot of credit.
Before I go any further, I have to point out that Star Trek:TMP was a kind of movie they just don't make anymore. It was done in a very "classical" style, where the plot and pace were less important than the themes, the visuals, and the feel of the movie.
If you want to understand what that means, fire up Netflix and select this movie. Then skip ahead to the scene where Admiral Kirk is shown the rebuilt U.S.S. Enterprise. Start at about the 15 minute mark. Crank up the volume on your TV as loud as you can get away with, sit back, and just watch.
Understand that this scene isn't just telling a story. It's reintroducing one of the most iconic entities in science fiction of the time, the Enterprise. It isn't just about Kirk seeing his old ship again, it's about the audience seeing her again for the first time since the original series was cancelled. It was about the new design, updated visuals from the campier look from the '60s to the sleeker, more subdued colors used in the film.
The visuals here are gorgeous, especially for the time. It really does look like this large starship is floating in space above the Earth. The effects showing Scotty and Kirk in the shuttlepod are a bit rough, but get past that and just enjoy the ship. Most of all, enjoy the music. Some of you may be surprised to recognize the score as being the same theme used later in Star Trek: The Next Generation, but it's an entirely different arrangement. In this sense, this theme represents not the movie, but Enterprise herself.
Pay attention to the soft strings when we first view the ship in the construction yard at about the 16:22 mark. We don't see her clearly yet, but clear enough to recognize her. We hear the theme song played slowly, letting us associate that theme with the starship for the very first time. Just watch, listen, and enjoy. Notice how Scotty glances at Kirk to see his reaction. That's the filmmakers looking at US to see OUR reaction.
"What do you think?"
Kirk's smile is what the filmmakers hope we'll have as they elegantly pan across the length of the ship, slowly revealing her a little at a time in great detail.
At about 17:50 we lose sight of Enterprise, and the music actually seems a little disjointed, something's missing...
Then Scotty turns the pod around... And *BAM* the theme comes back with a brass fanfare as we see the ship straight on. Access panels are still open, the navigational deflector is still dark, but that's Enterprise. We'd know her anywhere. NCC-1701 visible now under the saucer.
A little later, at about 19:41 we at last turn the pod to dock with Enterprise, and the strings are loud and sharp, playing the theme again with an emotion that's supported by the interesting camera angle, low and between the warp nacelles, showing Enterprise as she almost appears to be moving, the very design of the ship making the eye see movement. This is my favorite part, because the music really hits a crescendo here.
The sequence finally ends at about 20:40. Yes, it's a long sequence, over 4 minutes, just to show off the new ship. No plot development of any kind happens here, no important events, nothing to move the story... Just a visual and audio feast to celebrate the Enterprise making it onto the big screen and showing her new look to the audience.
Critics of this movie say it was a waste, that we didn't need to use up 4 minutes of running time just for that, but when you compare this to the Enterprise reveal in the 2008 Star Trek movie, this is way better. In the newer movie we get a glimpse as Kirk sees her for the first time, but it isn't really enough to appreciate the return of such an iconic vessel to the movie screen. It seems rushed and done almost just to get it done and out of the way.
For another treat, watch the Enterprise launch at about 34:40. Slow again, savoring the moment. Construction vehicles get out of the way, work lights are shut down. Enterprise is ready to go. There's the theme again at 35:09. Fanfare at 35:43 as she begins to move. We're being splashed with the theme now. This arrangement of the theme is very bold, optimistic, proud. The image at 36:47 as the sun rises behind Enterprise is possibly the most genius, beautiful effects shot of any space ship ever done in any movie.
(Notice in the Engineering section when Scotty is calling up to the bridge. That warp core look familiar? It was later used again as U.S.S. Voyager's warp core.)
Another note, when Kirk orders the ship to proceed ahead at warp .5, this is the first and only time sublight velocity is ever expressed as a decimal of warp speed.
Keep watching as Enterprise goes to warp. In terms of franchise history, this is the very first time we ever see a starship going to warp from outside the vessel. Skip to 39:55 to see it. Some people think it's cheesy and goofy but I think it's a LOT cooler than the weird rubber band look used in later Trek TV series.
So just keep these things in mind if you have an opportunity to watch this movie again. It's a treat for the senses. Not much of a story and slow pacing, but in my mind the artistry of it makes it well worth the experience.