Character mistake: During the scene with Kirk and Khan "space-flying" over to the Vengence, Bones loudly tells Kirk that he's "off course", with Karl Urban mistakenly falling into his New Zealand accent when saying "course."
Continuity mistake: After the Vengeance attacks the Enterprise and Scotty temporarily disables the Vengeance, Kirk and Spock head toward Sickbay. They pause in the corridor and have a brief exchange about "logic" and "gut feelings," with the camera cutting back and forth between Kirk and Spock. When the camera is on Kirk at first, the corridor behind him on his left is clear; when it cuts to Spock, a girl in a red engineering uniform with her hair in a bun and a glowing handheld device appears on Kirk's left and walks past, seemingly without noticing them. Camera cuts back to Kirk and the corridor is clear again. When the camera cuts back to Spock, the exact same girl with the hair bun and handheld device appears again on Kirk's left and walks past again, in the same direction as the first time, but this time looking over her right shoulder and into the camera. Camera quickly cuts back to Kirk and then to Spock, and now the corridor behind Spock is completely clear - the girl has vanished entirely.
Continuity mistake: Just before Spock and Kirk go to seek out Harrison, Kirk is examined by Bones. During the examination Bones is wearing a pinky ring, it's then gone, and then back again.
Chosen answer: The explosion of the Moon Praxis in the original Universe was due to extensive over mining and energy production. In the first movie that took place in the alternate reality, an entire Klingon armada was destroyed by the Narada. It is logical to assume that the Klingons began to over-mine the moon in order to obtain the resources necessary to replace so many lost ships, causing the moon to explode several decades before it happened in the Prime timeline.