Hmm...
Likes: I like the film's energy and pacing. I like the familiar feel of the characters if not always what they did. The performances of the familiar cast are generally good even if I question the actions of the characters. I like the look of the Reliant, a good variation of Starfleet design without looking like a kitbash (in contrast in TSFS the Excelsior is just damned ugly and the Grissom looks like a toy). I generally like Horner's score, but in a qualified way: it's good but it doesn't really feel like Star Trek to me. I prefer Gerry Goldsmith's TMP music that felt more like Star Trek on the big screen. I rather liked the Starfleet field jackets the crew wore. I liked some of the grittiness. I did like Kirstie Alley's portrayal of Saavik. Too bad she couldn't reprise the role later.
Dislikes: The story, for as has already been mentioned feels really contrived. Of course all fiction is contrived, but you should make an effort to avoid or minimize how obviously contrived it his. Numerous plot holes and logic flaws have already been mentioned upthread and I agree with them. I disliked the overt militaristic feel throughout. TMP got TOS' sensibility in regard to this better. I disliked how the ship battle was played out: it really felt more like two seagoing vessels battling rather than futuristic starships. I know Star Trek has done this before such as in TOS' "Balance Of Terror" but TOS still made it feel like starships and not naval boats. I hate the uniforms, they look ridiculous and more Honor Harrington than Star Trek. With the TMP uniforms it's the two-piece uniform I like and the one-piece not so much. I can agree with wanting more colour and style, but TWOK's uniforms were stupid looking as shipboard everyday service wear. I didn't mind Montalbn's performance of Khan when we first see him, but after he escapes the planet it's just pure ham, ham, ham. Khan in "Space Seed" had weight and presence, but after the introduction in the film Khan is an overdone caricature and not a worthy adversary. Finally I hated the whole training cruise scenario with the Enterprise a cadet ship. I wanted to throw Peter Preston out an airlock. It all smelled of a reset button after TMP. TMP had its flaws, but it nicely set the stage to go forward. TWOK feels like they wanted to rethink the whole thing and feels like a reboot of sorts.
I've enjoyed all the TOS based films to some degree or other when they were released, but the passing years haven't been kind in many respects. As such TMP DE and TWOK DE are the only films of the bunch I have in my DVD library. The rest just don't work for me anymore.