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.
Continuity mistake: When McCoy brought Kirk onboard a shuttle as a patient, they boarded a shuttle with round nacelles near the bottom. Most of the shots of it in flight show this. But the shot that zooms out from their window while heading to the Enterprise shows they're on a shuttle with wings near the bottom and nacelles at the top corners.
Continuity mistake: When young Kirk is driving the stolen car he unhooks the latches to the convertable roof. Cut to a side view when the roof flies off and we see that the car is kicking up a big cloud of dust from the roadway (so much dust that it looks like they cut from the paved road to a dirt road on the side shot, but the grass obscures the road top). Cut to a camera angle behind the car when the roof lands and the dust cloud has instantly disappeared, there is no trace of it.
Continuity mistake: During the scene in which Kirk first meets McCoy in the shuttle, watch the safety harness strap over McCoy's right shoulder. As the perspective changes back and forth from McCoy to Kirk, the strap is bunched up, then flat, then bunched and then flat again without McCoy touching it.
Plot hole: Despite their awareness of the red matter and the power of the singularity, no one on the bridge had the common sense to suggest pulling back to a safe distance. Nero had already refused their assistance so there was no need to stay so close to the singularity. And when a black hole was created inside Vulcan, an officer mentioned they had to reach minimum safe distance, so they know what they need to do, but no-one does it.
Continuity mistake: When Kirk, Sulu and Olson are space jumping down to the platform, they are shown on camera as falling with Olson in last place. He is furthest from the platform. Yet on Chekov's screen, he is displayed (by the red color associated with his red uniform) as being the lowest and closest, in first place.
Continuity mistake: When the USS Kelvin is attacked by the Romulan ship, there is significant damage done to the front half of the saucer section. However, after Ayel appears on the viewscreen demanding the captain, there is no damage or debris on the saucer section visible through the front windows of the bridge.
Continuity mistake: When young Spock approaches the three bullies at school, the shot from behind Spock shows he is at least as tall if not slightly taller than the other three boys. But when the shot reverses to see Spock between two of the bullies, he is instantly much shorter than they are. This isn't a matter of camera angle, but rather the choice to have young Spock positioned lower to make the bullies more intimidating - a choice the earlier angle didn't take into consideration.
Continuity mistake: After their discussion of younger Spock's emotional compromise, Spock Prime stays in the same spot while Kirk goes to the transporter pad. They are still talking as they do. Shots from afar show Spock is illuminated by the blue lights over his head as is the walls around him. But each time it cuts to a close up, he and the walls no longer show any hint of this blue. He also appears to be standing in a different location in the close ups.
Continuity mistake: When Spock points out to Sulu that he has forgotten to disengage the external inertial dampener, we see a close shot of Sulu as he corrects the situation on his controls, and Pike can be seen sitting behind him with arms by his side. It then cuts to a long shot where Pike suddenly has his arms crossed.
Continuity mistake: When Nero is (lying down? I can't tell during this scene) and waiting for Spock to arrive, we can see that he has a very faint tattoo of some kind beneath his lower lip. However, when he mentions to his first officer that he doesn't want Spock dead and wants him to watch Vulcan being destroyed, the tattoo has become black and very dark and also extends onto his lower lip.
Continuity mistake: As Kirk is being choked by a Romulan, he says "I've got your gun", then pulls the weapon and kills the Romulan. As the Romulan falls, Kirk grabs the edge of the platform and begins to pull himself up onto it. From well above, we see the Romulan's gun is lying on the platform pointing directly away from Kirk. But when the camera angle changes to show Kirk's face with the pistol between him and the camera, the gun now points to Kirk's left (our right).
Revealing mistake: When the Federation fleet is preparing to warp to Vulcan, you'll see the first ship blast off, but the second ship blasts off out of nowhere. You could argue that the ship was out of sight and below the Enterprise, but the light trail isn't that long. The light trail starts in front of the Enterprise where you should be able to see a star-ship.
Continuity mistake: When Kirk confronts Nero in person for the first time, one of the Romulans hits him and knocks him onto his back. Nero rushes over to attack him. The shot of Nero running over is an aerial view, and Kirk is seen partly trying to recover on his back. Clearly, his right arm is partly stretched up in the air and his left arm moving as he has his head lifted up. But the shot cuts to Nero getting to him in a close up and suddenly Kirk is totally flat on his back with arms down and head down.
Continuity mistake: While being sucked around through the aquatic gerbil maze of a coolant system in the Enterprise's engineering, there is one part where Scotty is being pulled up. The shot shows him get sucked out of the J pipe and begin being pulled up the shaft rather quickly. The shot cuts to Kirk yelling "No. No!" The shot then cuts to Kirk running off to the right, and it shows Scotty getting sucked out of the same J pipe a second time.
Continuity mistake: As Kirk and Spock Prime are arguing about Spock meeting his younger self, the shots from behind Spock show his hair, ear, and coat to be illuminated by a blue light. But the reverse angles have no evidence of this light at all. And when Kirk walks away, Spock is still standing in the same spot. Now suddenly Spock is all illuminated by blue lights that they were obviously not standing under moments before.
Continuity mistake: Right in the beginning of the scene where Kirk is taking his third attempt at the Kobayashi Maru, it starts out with Uhura telling Kirk what 'Starfleet' commands. Right as she finishes what she is saying, she cocks her head sideways to her right in an almost mockingly fashion. The very next shot jumps behind Kirk's shoulder with Uhura still in frame and her head is up straight.
Continuity mistake: After Kirk is in the bar fight, he is sitting down and talking to Captain Christopher Pike. Pike asks him a question and Kirk replies back with "Maybe I love it." The shot just before he says this is behind Kirk's head. Watch his head movements. He turns his head to the right, then straight again and tilts his head back some. Then the next shot where he says that line, he is suddenly looking down to his right.
Continuity mistake: When Kirk meets Uhura in the bar, there is an alien nursing his beer between them, and he never takes a sip, yet in one of the following shots, the beer is now significantly lower in the glass. The alien is in shot between Uhura and Kirk for the majority of the scene, and in the intervening shots, there is not enough time for him to have taken a sip of his beer.
Continuity mistake: After Chekov explains to Kirk his plan to hide behind Titan, Saturn's moon, Spock rejoins the group and tells them he will beam aboard Nero's ship. As he approaches, watch Scotty. The shot of Spock walking to the group shows Scotty has his head nearly straight, and his mouth closed. The shot changes to a close up on McCoy and Scotty is seen beside him. Suddenly, Scotty's mouth is open, and his head is leaning slightly more to his right.
Continuity mistake: After Spock chokes Kirk and then relinquishes his command due to being emotionally compromised, Kirk takes command of the Enterprise. As he sits in the captain's chair, he is still winded from the assault and is panting. Uhura walks up and says she hopes he knows what he is doing. As she says this, the side shot shows Kirk is looking straight ahead with his mouth open and leaning forward, panting. The shot then changes to Kirk in a close up and suddenly he is sitting back in the chair, looking more towards Uhura's direction, and his mouth is open less.
Continuity mistake: The first ship seen in the film is the USS Kelvin, which Kirk's father kamikazes into the bad guys' ship to save all the escaping shuttles. Later, Captain Pike is talking to Kirk about his father's heroic action and how he saved 'over 800' people from the Kelvin. So, since several died in the battle, that ship had to have at least 900 crew members. The USS Kelvin, a pre-alternate timeline vessel, is depicted as having a far larger compliment than the largest Star Fleet vessel (Dreadnought class, holding 500 people) from TOS times. Since the timeline had not changed at that point, this violates the "established" history.
Continuity mistake: Scotty is whizzing through the liquid-filled glass tubing and Kirk opens the release valve, saving him from his doom. When Scotty hits the floor, the camera pans across a piece of machinery, obscuring him for a second or two. When the camera picks up Scotty again on the other side of the machine, his arms are in a different position, bent closer to his body. Obviously a cut in the film where they removed the stunt person and replaced him with the actor to finish the scene.
Continuity mistake: Just after Nero's ship goes into warp speed to chase after Spock, the scene cuts to Kirk being confronted by one of Nero's men. Kirk jumps off the ledge of the platform and lands on another ledge. His arms grab onto the ledge with his arms stretched out. The next shot shows his arms now next to his body. He then stretches out his right arm to try and climb on some more. The next shot shows both arms stretched out.