To me, one real plot hole in the movie was when Kirk and Spock acted completely out of character in finishing off a helpless Nero. It bothered the hell out of me. Kirk didn't seem all that serious about rescuing Nero. And Spock's response was almost flippant. No debate.
-- OK, Nero destroyed Spock's planet of six billion people. So, does that mean Spock is entitled to go "thumbs up or thumbs down" on Nero's life? No rescue attempt. Instead, let him die. In fact, kill him. Spock is exacting his own kind of revenge on Nero. But is that in character? Even for the Spock in this movie? Revenge is not logical. Killing Nero does not bring Vulcan back. Spock, any Spock, knows that.
-- Even Kirk knows that. Instead it's Kirk as executioner. What will he say in his log? That they decided not to try to save Nero and his crew? Instead, they actually opened fire on his ship as it fell into the black hole? Kirk was a warrior, and he killed, but he had no bloodlust. He didn't kill if he didn't have to. He never destroyed a helpless enemy. Apparently, like the Klingons, this young Kirk doesn't take prisoners.