It's been a while (since it was in theaters, really), but from what really irritated me about STID:
-Kirk's death scene was lifted almost verbatim from Wrath of Khan. I was actually quoting Wrath of Khan in the theater, and almost got it EXACTLY as they were saying it on screen. (Yes, I've seen WoK that much).
-magic cure-all blood
-can't beam moving objects (still a gripe in the first movie too)
-Emo Rage Spock again
-warp speed contrails. Why? It's warping space, so why is there exhaust??
-Chekov as a boy genius engineer when that's not his training and there are more qualified officers there...like the assistant chief engineer
-iBridge by Apple
-lens flares
-Enterprise hiding underwater. That was just stupid. It was done just to look cool. A starship isn't designed to be underwater. They could've just taken a shuttle. What irritates me about JJ-verse is that things happen because they look cool, not because they make sense or would be in any stretch logical or realistic. (yes, I know it's sci-fi, but at least most of Trek has been logical enough to suspend disbelief).
-the Klingon. Uhura's pronunciation hurt.
-Kirk's quick promotion to starship captain, even quicker than in TOS, still is baffling in an organization that seems more military than TOS. This Kirk is less than a tenth of the officer that real Kirk was. Real Kirk might've bucked rules, but there were just about always extenuating circumstances justifying them. Look at Court Martial and Where No Man Has Gone Before. They establish Kirk more as a by-the-book kind of officer who goes by his training. This new Kirk seems not to be as rational or capable an officer in comparison. I could make a more effective comparison by watching the movie again, but then I'd get mad at it all over again.
-Vengeance starship design, kind of looked like a bottle opener, and it's ridiculous to waste space by making the saucer a ring instead of a saucer. How much longer from the forward-most point on the ship would it take to get to the bridge in an emergency in such a ship? Structural stresses? Why's there a set of moving plates over the deflector? What if they get stuck?
-emo-witch Uhura bringing her personal garbage onto a mission, interrupting a mission. Wasn't she trained at Starfleet Academy not to bring your personal baggage to work? Isn't everyone? This Starfleet seems more military than even TOS did, so I'd expect the personal baggage crap to have been trained right out of Uhura during basic training.
-Uhura-Spock still makes no sense, even moreso now that there are supposedly only 10,000 Vulcans left (what about all the Vulcans on starships, on Earth, elsewhere? That's got to be several tens of thousands more). It would be logical that Spock find a Vulcan female when Pon Farr hits.
-Enterprise still is a mis-shapen mess. Engineering juts forward too much, nacelles are too big for the pylons, the saucer is too big for the engineering hull, there's a brewery where engineering should be, and did anyone else notice the giant gaping hole in the middle of the saucer inside?? How did anyone decide that (a) wasting that much space was good design, and (b) wasting that much space with open air would be safe in an environment with variable gravity? Besides...being a waste of space...it's completely unsafe, causing a number of railing kills (MST3K reference).
If I were to watch it again, I could come up with even more.
The good part though:
-dress uniforms vs duty uniforms. I really really liked the dress uniforms as an homage to TMP, and for looking like dress uniforms, esp. with the cover.
-aliens seem to be more present in the crew, showing the Federation as not just a "homo sapiens only club."