In the event that you haven't seen it:
Honestly, the trailer had me at the Spock-McCoy "at least I won't die alone" sequence. I had a big goofy grin on my face at that bit, which was just perfect. It's also one of the few actual dialogue sequences we get, and if it's indicative of the rest of the script, I'm not worried.
The main problem with the trailer, and it's a big one -- and I honestly think that it's half the reason why people are complaining about it -- is the music, which is horrible. Luckily, the companies that put trailers together don't (necessarily) use music from the film (otherwise, every other drama would have "Solsbury Hill" in its soundtrack).
But the rest of the trailer looks promising. Yes, it's almost entirely big-ass action sequences, but so's the trailer for the final Hunger Games film, and I don't see anyone saying that that's just a dumb mindless action movie. It's a summer science fiction blockbuster movie, of course the trailer is emphasizing what's visually exciting and is low on plot. That's SOP for such trailers in the early part of the 21st century, and I don't see why Star Trek should be exempt.
Of course, all the usual complaints are coming out of the woodwork, most directed at JJ Abrams, and generally talking about how they should hire people who care about Trek to do the films, as if that matters. You know who cared about Trek? Gene Roddenberry, Robert Wise, William Shatner, Jonathan Frakes, and Michael Piller, who were responsible for The Motion Picture, The Final Frontier, and Insurrection, three of the absolute worst of the Trek films. You know who didn't care about Trek? Nicholas Meyer and Harve Bennett, who gave us The Wrath of Khan, generally considered the best Trek film (so much so that both Nemesis and Into Darkness basically copied it).
Look, it's a Trek movie, so it's never going to be Trek at its best in any case. Star Trek is a TV franchise, and has always been at its best in that medium. The best Trek movie can't even crack the top 50 of best Trek stories when the TV medium has given us "The City on the Edge of Forever," "The Trouble with Tribbles," "Balance of Terror," "The Inner Light," "Yesterday's Enterprise," "The Best of Both Worlds," "The Visitor," "In the Pale Moonlight," "Tacking Into the Wind," "Year of Hell," "Jetrel," "Judgment," "Demons," "Terra Prime," etc.
If nothing else, the 2009 film and Into Darkness proved that this cast can deliver a fun film, and the one element of the previous films that was disastrous -- the script -- is being handled by someone else this go-round, so they've actually fixed one of the things that was broken and we still have this cast, thus keeping what worked. For that alone, I'm very much looking forward to seeing it.