Continuity mistake: At the end of the film when Kirk is being awarded his medal, behind the Federation Counsel you can see 3 flags in the background- the center flag is the California state flag. After Kirk shakes Pike's hand, and the camera pans up and back, the California flag is hanging significantly different so that it is no longer recognizable, seeming almost blank white. As the ceremony is indoors and all attending are standing motionless, this flag should not have moved.
Continuity mistake: When Kirk is sneaking about on the Romulan ship, just after Spock takes off in the ship, we see a shot of him walking down a dark corridor, carrying what is very clearly a Romulan pistol (quite long and thin). When the shot changes, he suddenly has his standard Federation Phaser in his hand when he confronts Nero. He doesn't get a Romulan pistol like that until after the fight with the first officer, when his phaser falls over the edge.
Question: What was Nero doing for the 25 years between his attack on the Kelvin and the one on Vulcan? Additionally, how did he know when and where Spock was to appear? Did he sit his ship in front of the black hole for 25 years? And why was his ship armed to the teeth? It's supposed to be a mining vessel.