I could go on all day about the plot holes and how nothing makes sense. But that's too easy. I like for a moment to go deeper. In the trailers and the movie itself, there's a quick 2 second shot that baffles me. No spoilers since everyone can see it in the trailers~
In this scene the big mean enemy ship is shooting the crap out of the Enterprise with the moon as the background. (you can guess what part of the movie it's in from that) While firing the standard red phaser 'bolts' it's been using this whole time, we catch a fleeting glimpse of some... blue pod. Here:
It fires what look like three WHITE missiles with smoke trails at the nacelle, primary hull and secondary hull and then passes close to the screen in a blur (pic4) before the missiles detonate, doing considerably more damage than even the red phaser shots! (timestamp 2:14 on trailer #3)
What the heck is this thing?! Some kind of attack drone? Is it another weapon system designed by Khan? If it goes dormant when their weapons get taken offline, why can't Khan restart it and have it blast the Enterprise to dust while his ship goes down? It seems like something really interesting that was just cut out but left in for a moment or two because they didn't think people would notice.