The first of JJ Abrams' reboot of the Star Trek franchise was pretty lame, but could have worked to reboot the series. He took everything that was important and mythic about the Rodenberry tv show and subsequent movies and flattened it into a buddy film with familiar catchphrases. Still, there was lots of action and the characters were set in motion.
A second movie might have been risen above the first. After all, most of the ST movies weren't particularly good. The notable exception: Star Trek II: The Wrath of Khan, which rose above the first movie and built on strong characters and story arcs from from the tv show. Just a few years after genocidal megalomaniacs like Stalin and Mao, Khan is a villain who is at once horrendous and heroic. He had a place in the Star Trek backstory, and illuminated Rodenberry's vision of the future.
So along comes Star Trek: Into Darkness. Dreadful, just dreadful. Even the name is stupid. I suppose they couldn't call it Star Trek II: II. It's a reboot of Wrath of Khan, and gets everything wrong.
In the original Wrath, the takeaway is: Life is important, and even the bad guys deserved a chance. In Darkness, the takeaway is: Some lives are more important than others. Hundreds, if not thousands, of people die, but as long as one of them is not Spock or Kirk we can be happy.
Khan is reintroduced first as a good guy, a special agent. We quickly learn that he has gone rogue, and blows up an archive, which turns out to be a secret archive, which turns out to be where they've stored his "people". Yeah, that's how to save them: Blow up the installation where they're kept.
At no point is Khan or "his people" explained. I suppose they just left it to the fans to remember the Eugenics Wars of the 1990s. But unlike Wrath, where mutants escaped and were lost to history until encountered by Kirk and crew, Khan and the mutants were put to work by the government. Who (major SPOILER) is desperately trying to force a war with the Klingons.
Yeah, like you have to be sneaky to get into a war with Klingons.
Khan's 72 people are frozen and put into missiles which the Enterprise is almost tricked into firing on Kronos, the Klingon homeworld. Why you needed people in missiles is never explained. The whole freezing technology is explained very badly: The current Enterprise can't help the people in the missiles because freezing hasn't been used since warp technology was invented. By itself, two major plotholes: Not only would they have digital records of such things even if obsolescent, but the technology is incredibly useful for other things besides space travel. Indeed, one of their first impulses is to put the dying Kirk into one. But I'm getting ahead of myself.
[ETA] The point of timeline change for the reboot is Nero's destruction of Vulcan in 2233. So any Star Trek canon before that is, in theory, still extant. So that leaves Khan and crew in space, having launched from Earth in the 1990s. Unless you want to argue that Nero completely created a whole new timeline from scratch, which has it's own major problems, this oversight is a major hole in Darkness.
So anyway. After Kirk is relieved of command because of stupidity involving a choice between saving Spock or following the Prime Directive, there are explosions and some plot and Kirk is back in charge of the Enterprise. He's desperately chasing this guy Khan, about whom nothing is known. Khan has fled to the Klingon homeworld, because that's the last place the Federation would look. Heck, they might start a war. But Scotty figures it out, and they go anyway.
Precisely why Khan, a very clever villain who has been hiding on Earth for a long time, wants to go to Kronos is not explained. When the Enterprise gets there and Khan finds out they have the missiles which (unbeknownst to Kirk because he didn't listen to Scotty) have Khan's crew, Khan promptly surrenders.
Khan saves his frozen missile-bound crew, war is averted. So all that remains is for Khan to trick Kirk into... um, well, exactly what Khan wants is unclear. He wants his crew back, but never seems to go so far as to try to get them out of the missiles. Some lives are more important than others, but unlike Ricardo Montalban, who got to chew the scenery about his lost love, Benedict Cumberbatch (Sherlock Holmes on the BBC) gets to threaten McCoy and trick Kirk.
Meanwhile, Admiral Marcus, the head of the Federation who wants war with the Klingons, has brought out his ultra-secret super star ship to chase after the Enterprise. Fortunately for us, Scotty is on board. Precisely how Scotty gets on board the highly guarded ship is never explained. And Marcus doesn't bother to actually start the war he's wanted, he just wants... well, exactly what Marcus wants is unclear. He claims to want war, with him in charge, and has spent untold billions of Federation bucks (or whatever they use for money) and hired mercenaries to build the missiles and super starship. But all of this was done in secret and (it's implied) illegally. His plan is thwarted because his beautiful and brilliant daughter has lied her way onto the Enterprise, so he's reluctant to kill everyone on board. Some lives are more important than others.
There's a warp drive chase scene, Marcus kills a bunch of Enterprise crew, Kirk and Khan form an allegiance and jump from the Enterprise to the larger ship. Good thing we have Scotty on board to press the right button at the right time, opening up the access port, killing the mercenary who doesn't seem to realize that Scotty is not one of their small, tightly-knit crew. The death of the mercenaries happens without comment and without tears. Some lives are more important than others.
More explosions, and Marcus' treason is stopped, but Khan refuses to die. Khan doesn't realize his crew is still alive (though frozen) and very mad. Now, once we heard the name "Khan", we knew exactly what would happen to Kirk and Spock, and could probably guess the twist. Khan wants revenge on the Kirk and the Federation. He destroys the Enterprise even more than it was destroyed by Marcus. This leads to Kirk on the inside of the radioactive engine coils. In a stark parallel to Wrath, Kirk saves the day but dies while Spock on the outside. They hold up hands to make contact through the safety glass. Kirk dies, and Spock lifts his fist to the air to utter, "... Khan!!!".
Really makes one appreciate the acting abilities of William Shatner. Seriously, it's a defining moment of the Star Trek franchise, and Shatner was great and Quinto was a pale imitation. The horrible editing doesn't help the moment either.
So anyway. It's still 24 time. Khan's well-laid plans for all contingencies don't seem to include a base of operations after he gets his crew back. He's left with plowing the super star ship into Federation HQ in San Francisco. Lots of death, but the main concern is keeping Khan alive so his blood, which has revived a dead tribble (yes, you heard me) can revive the dead Kirk. Some lives are more important than others.
There's a nice chase sequence from moving air car to moving air car. Why there are is anything in the air after a terrorist attack from the sky seems stupider than usual, but hey. It's less exciting but more believable than the one in the Matrix movies. Spock and Uhura get to prove they can be professional and lovers. Khan is subdued (but not killed), Kirk is saved.
I don't recall what happens to the 72 frozen Star Seed. Probably not explained well, if at all. Kirk gets his command of the Enterprise back, in a brand spanking new ship (with the same registration number). And then Abrams blows it again, completely wiping perhaps my favorite line in all the Star Trek movies: When Shatner/Kirk gets his command back (at the end of III or IV, I forget), and the crew asks what heading he wants, he casually said, "Oh, thataway". At precisely the same moment in Darkness, with a great deal more build-up, the moment just passes. Pine/Kirk is just flat.
You can make fun of Shatner's broad acting all you want, but at his best he was a great Kirk. And he was at his best a lot.
The original Star Trek was very much a product of the Cold War. The reboot is very much a product of the post-9/11 world. We were in greater danger from the Russians at the time, but more easily wet our pants at potential terrorism. We now produce films that rely on post-attention-span, sphincter-clenching action. Bah.
Leftover bits: Leonard Nimoy makes a brief appearance, breaking his vow from the first movie not to reveal any plot points. The 3D was okay, but probably unnecessary. Nothing extra happens after the credits.
Anyway, just to be clear: I didn't like the movie.