I think Khan was using whatever he had left to try and crash into Starfleet HQ. (Man they need to put some shields around that thing .) It's more bothersome that two starships are battling it out just past the moon, and there aren't any other ships in the system that can help the Enterprise?

Might have been better for Khan to splash down in the middle of the bay and have the obligatory fight with Spock as the wreckage of the Vengeance is sinking.

Why does Admiral Banzai Paxton Marcus need a genetic superman from two centuries ago to design scarier ships and weapons anyway? Wouldn't kidnapping old Spock and forcing him to divulge 24th century tech make more sense? Starfleet bigwigs must know where Scotty got his transwarp beaming equations from.

Interesting that they did deal with the issue of asking old Spock for info on old adversaries.