A Constitution-class? Maybe if this were the Prime Timeline. Unless the ship was severely warped coming down before crashing, that's not the Enterprise crashing. Nacelles are too widely spaced, the nacelles themselves have an oval look to the front of them rather than a round look, the pylons are shaped wrong, nor do the engines have our beloved 1701's trademark fins. Not the Enterprise. Besides, if you look at the trailers, you can see that the nacelles are being shoved forward from the impact(obviously not a safe water landing, but a head on collision with the bay). This doesn't hold up with the idea that this shot is connected with the shot of the Enterprise rising OUT of the water since THAT shot shows the Enterprise in perfect working condition. Scotty's good, but he's not THAT good.
Speaking of, if the Enterprise WERE going to be destroyed, I don't think Scotty would be that calm about it. Not young Scotty, at any rate. The fact that he's comforting Uhura, who is turning away from whatever they're looking at, implies that they just watched someone get their butt kicked and/or is being tortured.
As for shots of the "bridge" blowing up...unless the Enterprise had a tremendous refit and installed a large table with laptops on it, that's another shot not taking place on the Enterprise. In fact, the Enterprise herself was only seen once in an external shot, and a couple of times internally. No space shots either.
Also, there were indeed Klingons in several shots, so while they may not be primary antagonists, they will play a role in this one.
Now, I do think it's very probable that Alice Eve is either a revamped Carol Marcus or Elizabeth Dehner(hairdo points to the latter). However, I am not so sure about Cumberbatch being god-like Gary Mitchell. On one hand, it seems extraordinarily likely. But there are a couple of problems with that. The first of which being the comics. They already did "Where No Man Has Gone Before". Mitchell is dead. So unless he was PLAYING dead so Kirk would leave him, I certainly don't buy him coming back, though a phaser rifle might NOT have killed him. But still. If it is Mitchell, how are they going to explain all of that without a massive recap for the non-comic reading audience? Also? Aside from being exceptionally strong, I haven't seen a whole lot to indicate that he alone is responsible for the chaos occurring. Finally...no glowy eyes. At all. None. Now, that's not to say it's not likely. But I'm pointing out the facts that dispute it. For all we know, it could be Captain Garth.
Finally, as for the extra bit at the end of the Japanese trailer...while I think that it's meant to evoke that famous scene in The Wrath of Khan, it's not Kirk and Spock we're seeing here. It's definitely Spock, he's doing the Vulcan hand gesture, but he's in his Enterprise uniform. The other hand is in a black outfit. I think we might be seeing a bit of what happened to cause all of this because we see Cumberbatch in a black uniform a few times. I don't think they would pull that kind of stunt on us again. Especially since, I believe, the main crew is contracted for another movie beyond this.
As for what I think of the trailer itself? While I'll admit to some disappointment that there's only one real shot of my favorite starship and only glimpses of her crew outside of Kirk, Spock, and Uhura(Bones, Scotty, and Sulu make very brief appearances and I didn't see Chekov at all, let me know if you guys did and I'm just blind), I have to say, I am really excited for this. While the vengeance bit is getting a bit stale, it seems like this one's going to be a little more impactful than Shinzon or Nero. The fact that Cumberbatch is human and a former member of Starfleet adds to that. And I personally think that the scene with the Enterprise rising from an ocean is going to be the crowning effects shot of the Enterprise for this movie, much the way the Enterprise rising from Titan and being framed in front of Saturn was for the previous movie. Also...the most lens flares seemed to be either in the title sections or when the sun or other actual light source was visible. Not counting weapons fire, of course. All in all? I can't wait for the longer trailer coming with The Hobbit.
EDIT: Also, with Cumberbatch's voiceover being the first I've actually heard from this actor(haven't seen any of Sherlock), I am even more excited about The Hobbit as well since C-batch is also doing the voice of the dragon Smaug. He has a nice, deep, booming voice.