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.