Although a bunch of random theories are bouncing around in different threads, I thought I'd try to give them a dedicated thread. And to start things off, I'll post my own belief of what STID is about
In 'Countdown to Darkness #3', a bunch of new info is revealed. We learn Robert April is supplying weapons to the losing side of a warring race -- their opponents, who would have otherwise committed genocide without April's intervention, are being supplied weapons by the Klingons.
We also learn that April is willing to risk putting the Federation at war with the Klingon empire by using the Enterprise's weapons to destroy the opposing alien army. He seizes control of the Enterprise by activating a sleeper program that gives him sole access to the ship's systems -- an algorithm carried over from the old Enterprise, which he said "I'd never lose my ship!"
So, my theory: the mystery Constitution class ship we see in the previews, the one which crashes into SF Bay, is April's Enterprise. And the person who commands it is April -- but not Robert. Rather, it's his son: John Harrison April. He will stop at nothing to destroy the Klingons, because he blames them for the death of his father (I think we'll see Robert April killed in issue #4). He's willing to put the entire Federation at war in order to wipe them out.
This nicely explains a number of things from the trailers, including why Harrison is sitting in a command chair that isn't obviously the new Enterprise's. And also, it gives very deep meaning to his voice-over line "is there nothing you wouldn't do for family?". Lastly, it explains why the prop in the Bad Robot offices was labeled "April's Gun". It is April's gun, just not the April we thought.