The start of the film is filled with massive plot holes and problems.
The gross violation of the PD is a biggy though.
It really isn't. It happened all the time, in every iteration. The TNG cast were the only ones to do more than pay lip service, and even they ignored it pretty routinely.
This notion of the prime directive as an inviolable rule, not just of the fictional institution of Starfleet, but of real people who intend to write a story set in the Star Trek universe, is a fan made notion that I don't recall ever existing before Into Darkness.
Yea, my interpretation of the Prime Directive has always been "Don't interfere or you will be required to defend yourself". So, a Captain, can violate The Prime Directive, if he thinks it's appropriate, and he will be judged after the fact if he made the right decision.
One Day I hope to be the Man my Cat thinks I am
Where are we going? And why are we in this Handbasket?