The worst offender is, of course, the extreme plot coincidence that sees Kirk being set down on the icy planet within about half a mile from Spock's cave, and then finding that cave by chance. Out of all the land area on the planet he could have been placed on, being put there at random stretches plausibility. Then, because in for a penny in for a pound I suppose, they also happen to be close to a Federation outpost where of all the people in the galaxy, Scotty is coincidentally posted. A plot probably shouldn't need that level of coincidence to work.

There's also the notion that the bad guy blamed Spock so thoroughly that he destroyed Vulcan. He did this because ... Spock tried to save Romulus and failed. Would it have been better if he had never even tried? That's utter crazy person logic, and if he's a crazy person then he's less interesting than a villain who has actual real motives.

Did the movie explain the whole Romulus destruction thing? Were all the people on the planet killed? If Spock had time to rig up his red matter machine and warp there, wouldn't there have been a chance for lots of starships to beam as many people as possible off? Did the sun go supernova without warning? If all the people weren't killed, how is it justice to kill all the people on Vulcan? I don't even really remember if any of that was explained, but I suspect it was glossed over.

Back to coincidences, it's a fairly big one that Kirk happens to be randomly jumped up to a high enough position that he can take command of the ship on his first actual assignment, instead of earning it or at least having all the higher ranked people killed somehow.

Don't get me wrong, I actually like the movie, and found it entertaining, and will watch more and applaud the style and fun on display. But it wasn't the most structurally sound plot ever conceived.