These are what we call the 'YMMV items.' Things that some people find in this work. We call them 'your mileage might vary' because not everyone sees these things in the same way. This starts discussions in the trope lists, a thing we don't want. Please use the discussion page if you'd like to discuss any of these items.
"Ilia's Theme" is one of the most stunningly beautiful pieces of music in all of Star Trek.
The Klingon battle theme towards the beginning, which would also be used as Worf's leitmotif in the TNG films.
The La-La Land three-disc expansion is a must.
Ho Yay: "This simple feeling..." is exactly what, now, Spock? Especially since they're holding hands? And Kirk's gazing at him with a look of unprecedented, almost aching tenderness?
Well worth noting: Hand touching is Vulcan kissing. Yeah.
"Dammit Bones, I need you!Badly!"
The page image for Ho Yay is from this movie. Just sayin'.
Watch the scene where Spock first shows up on the bridge. Now look at Kirk's face. Does he or does he not look like he's just had the love of his life returned to him from death? His entire face lights up in that moment. There's no ambiguity there whatsoever.
And V'Ger finally understands this 'simple feeling' once Decker and Ilia join with it...sorry, is this supposed to be subtext?
As awesome as the effects in the theatrical cut generally are, there are a few cases where it's obvious that the effects were rushed in order to meet the release deadline. Notable examples are the horrible-looking asteroid explosion, and two occasions later in the film where V'Ger's energy bolts are rather clumsily matted in. Also happens literally. The first special effects company couldn't get the job done, so Douglas Trumbull and John Dykstra had to be hired late in the production.
In the TV edit which aired several times on ABC in the 1980s, one notorious scene, in which Kirk spacewalks out of the Enterprise to join Spock at the meeting with V'Ger, features an unfinished wide shot of Kirk leaving the ship, with the studio rafters and scaffolding visible all the way around the edge of the "ship exterior". The scene had been cut during filming but was restored to pad the TV edit before anyone realised that it had not undergone any post-production.
It also didn't help that the scene was part of the original space walk, in which Kirk joined Spock and encountered a "memory wall" together. The spacesuits were significantly redesigned between the filming of the original scenes and the final version of the "Spock Walk".
Visual Effects of Awesome: Powered by going way over budget. From the iridescent paint job on the Enterprise that made Chroma Key fail hard to zillions of vehicles and costumes you only saw on screen once to (of course!) the mind-bending V'Ger sequences, you should seriously consider giving your eyes a break every now and then.
Not to mention the AWESOME effect when the Enterprise warps out.
Supposedly, Robert Wise had the uniforms designed so plain compared to the bright TOS uniforms (which were planned to be used again in the Phase II series), so that the audience would focus more on the actors' faces. Unfortunately, the actors didn't get to show a whole lot of emotional range throughout most of the movie, so the ploy ended up backfiring spectacularly.
Freud Was Right: Everything has sexual subtext. EVERYTHING. Enterprise has make-out alcoves, V'Ger's giant orifice is likened to... another kind of orifice, Kirk gets a boner while talking to an old flame, a pretty intimate description of Probe!Ilia's first appearance, V'Ger wondering why Decker and its probe are having sex (Decker suggested it as a way to break through to Ilia's mind and Kirk agreed to it), and on and on and on.
Ho Yay: The movie is already fairly homoerotic, but the novelisation takes it Up to Eleven. For one thing, the novel introduces the Vulcan word t'hy'la, which Spock uses to describe Kirk, and which can mean friend, brother or lover. For another, it outright states that it was Kirk's mind that had called to Spock across the lightyears and ruined his Kolinahr (the film implies, though doesn't outright state, that it's V'Ger's arrival in Federation space which disturbs Spock during his Kolinahr). For what it's worth, the novelization was written by Gene Roddenberry. Yes, that Gene Roddenberry. (Roddenberry did this, in part, as an act of revenge against the film's screenwriter Harold Livingston - Roddenberry really wanted to get script credit but didn't (and turned down co-story credit), so he got his own back by novelizing the script, as was his legal right. It's worth noting that Livingston and Alan Dean Foster (who has story credit) aren't mentioned on the front cover.)