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: 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.
Other mistake: After the Enterprise is disabled by the Vengeance and falls out of warp, Kirk and Spock have a discussion in one of the corridors about letting Khan help incapacitate the attacking ship. Watch behind them. The ship is running under Red, but the crew members are walking past them calmly, some even watching their conversation as they pass! Not really Red Alert protocol... In fact, through all of this, only one crewman runs past in the entire sequence.
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.