One of these things is just like the other
There are a few instances of mirroring; in addition to the most obvious one, where they seem to be homaging Spock's death scene from Star Trek: The Wrath of Khan, you get a couple of spots where Abrams mirrors himself as well. First of all, there's a shot of Kirk and McCoy running from something or another; they're wearing robes and they leap off a cliff, which serves as kind of a visual callback to the car going over the edge in Star Trek. There's also a sequence in which Kirk stumbles upon Cumberbatch on the bridge of (his? another?) ship, where Cumberbatch is in the Captain's chair wearing a Starfleet uniform. This is a bit like when Kirk himself commandeered the captain's chair in the first film. There's also a look at a Starfleet vessel rising up out of the water near the beginning of the trailer, which mirrors what looks to be the Enterprise crashing down to the water at the end.
Funeral for a friend?
You've also got Kirk speaking at a starfleet ceremony -- likely a funeral, since the plot synopsis for the film hints to a major attack on Earth in general and Starfleet in particular in this film. There's always the possibility that if it's not actually Kirk or Spock who appear to be sacrificing themselves in that Japanese-exclusive scene from the trailer, this could be mourning whoever did.
A better shot of Spock in the volcano comes along, and one that gives us a bit more context (but not much). It's still unclear what exactly he's down there for, although our smart money is on something like trying to detect a bomb that our terrorist bad guy has placed in the volcano, which could create a really catastrophic scenario if it goes off. That equipment he's carrying sure looks like a "we're looking for something" box. Apparently a bunch of the movie will take place on earth, as evidenced by the fact that we see Spock chasing Cumberbatch's character through city streets at one point.
We do get a few quick looks at Alice Eve, who will apparently be the new object of Kirk's affection. We don't learn a whole lot from her or any other new character beyond Cumberbatch's villain, since he's the only one whose voice we hear in the whole minute plus.
Bring on the bad guy
When we actually SEE Cumberbatch, he's got a giant gun of alien origin. Commenters are already thinking the gun could be Klingon in origin, which of course jives with the helmet/character we've already seen teased.