Please.
Plotholes after plotholes after plotholes after idiocies after contradictions, is the first problem, starting with the very first dialog, not a minute into the movie.
"It's like a lightning storm in space. You should see it!"
"We're not yet in visible range, captain."
Seriously, you can try to warp that as much as you want, but getting those two sentences to function in that order, will lead to failure. And there's more, so much more:
A complete asshole as the main character that doesn't do anything throughout the movie except running after the facts.
Major character development in major characters that aren't character development, it just happened by writer's fiat. I'm looking at you, Spock, who before only acted upon attraction to females that are perfectly legitimate mate-material when he got his brain addled either by the natural Ponn Far or space spores and drugs, is now in a relationship with one of his STUDENTS.
Supposedly logical and intelligent Vulcans sending "we have seismic problems" as opposed to "Help, we are under attack", when the attacking ship and the giant ass drill beam is seen by people with their own, naked, unhelped by instruments eyes.
Communications officers in an entire fleet that are apparently completely incompetent as none of them remarked to their captains that THERE WERE NO SIGNALS AT ALL COMING FROM THE VULCAN SYSTEM AT ALL. To such a horrifying inept extent, that when one is asked to see if there are any signals with Romulan language coming it, he spends his time jabbering about being unable to differentiate Romulan from Vulcan instead of telling Pike THERE WERE NO SIGNALS AT ALL COMING FROM THE VULCAN SYSTEM.
The same scene is all about Kirk convincing Pike this is a trap with a level of illogic that is breathtaking to stop the Enterprise from dropping out of warp in the Vulcan system and avoid that trap, only for once he finally succeeds and they drop out of warp... them being in the Vulcan system and in the "trap". Making the entire scene POINTLESS.
Brick walls on starships.
Spock goes to beam down to save his parents! Kirk and Sulu are falling! Chekov has a solution! He runs not ten meters from the bridge into the transporter room! He saves Kirk and Sulu! ...Spock arrives in the transporter room that is ten meters from the bridge, despite him leaving the bridge before Kirk and Sulu are even falling.
Kirk doing more assholery making Spock shoot him out the ship down to a planet, presumably having to change course to get to that planet, while time is desperately of the essence, as opposed to simply throwing him in the brig; being every bit as much the idiot that made him arrive in the transporter room after Chekov gets there and saves Kirk and Sulu.
Kirk meeting old Spock and Scotty on the same planet, apparently because of destiny, and destiny wants Kirk as the captain of the Enterprise, apparently. Apparently it wants that only after Vulcan got blown up, and put Kirk in command of the enterprise years before he got there in the time line destiny wants to preserve. Which begs the question why this nebulous "destiny" didn't simply destroy the Narada before it could muck up "destiny", or do something else before Vulcan got destroyed, or better yet, made sure time travel travel is impossible to begin with!
But wait! We're not there yet! Because according to the movie, the writers, the director, this is an alternate reality, one that got split off once the Narada arrived in the passed and mucked things up. Thus, this alternate reality, and its destiny has absolutely nothing to do anymore with the prime universe. Result being, that whatever happens, if that is the destruction of Vulcan, Earth, Starfleet being annihilated, Kirk not only not getting command of the Enterprise, but not even graduating, so be it, and "destiny" couldn't care less, or in fact, be working to make that outcome come true. Which makes the whole "destiny" crap just plain idiotic.
But wait! The worst offense that "destiny" made is still yet to come. You see, Gene Roddenberry was a secular humanist, before the term even existed. His Star Trek and the subsequent series are infused with humanism throughout. There are no gods, no invisible flying spaghetti-monsters, destiny, or other nebulous invisible supernatural forces mucking with human decisions. No, WE humans and other sentients, did it all ourselves. It is the very heart and core of Star Trek that has been uphold throughout its existence, until JJ's Trek Wars.
Bravo.
And all of that is just the beginning, the horrifying "science", the idiocy of a captain having a code that shuts down an entire solar systems defensive systems, a cadet being promoted to captain, and on, and on, and on. I've barely begin to name all the problems with this movie.
They aren't simple "I didn't like it", they're flaws, plot holes, bad writing, idiocies, and what not.