Continuity mistake: In the bar, Pike meets up with Kirk to tell him that they gave him the Enterprise. When Pike tells Kirk that Spock has been reassigned to the Bradbury, Kirk pours liquor into his glass, nearly covering the big round ice cube. When Kirk lifts the glass from the bar, half of the liquor instantly disappears. (00:19:20)
Continuity mistake: As Kirk and Spock converge in the lobby of the Daystrom building, Spock greets Kirk with "Captain" and Kirk responds "Not anymore Spock, First Officer." There is a cut between "Not anymore" and "Spock." During the cut Spock moves from being in front of Kirk to behind him and the two have moved from the middle of the lobby, with the ramps visible 10 to 15 yards ahead of them to right beside the ramps. (00:22:15)
Continuity mistake: After Harrison (Khan) has attacked the senior officers' meeting and Pike has died, the position of Pike's head on the cushion changes between shots. When Spock disconnects from the mind meld, the stitching on the cushion is above Pike's ears. When Kirk checks for a pulse, the stitching is below Pike's ears. The angle of his head also changes. (00:28:05)
Continuity mistake: Admiral Marcus' ship "The Vengeance" comes out of warp and immediately appears to be right beside the Enterprise. The top of the ship even goes over the roof of the Enterprise to prove it. Yet from an immediate side angle of the two ships, the distance between the two ships has increased noticeably and the Enterprise is now facing towards the Vengeance. (01:12:55)
Continuity mistake: When Admiral Marcus' ship appears in front of the Enterprise after coming out of warp, a set of panels begins to close over the main deflector dish. In the next shot, when looking out of the Enterprise's viewscreen, the deflector dish is fully visible again. (01:13:05)
Suggested correction: This detail was intentional. As a purely military-minded ship, the Vengeance was built with many different defense mechanisms, including the ability to protect its deflector dish by opening and closing a pair of panels. It simply closed them for protection, then opened them again when the deflector dish was needed or the Enterprise was no longer deemed a threat.
The problem is that the doors are shown closing, and then in a split second, when seen from the perspective of the Enterprise, they are still open.
Continuity mistake: When the Enterprise is spinning out of control, Spock and Sulu activate their seat belts across their shoulders, but Sulu's disappears shortly afterwards, only to reappear seconds later. (01:41:05)
Continuity mistake: During the USS Vengeance's planetfall, just after it passes over Alcatraz Island, the fort is visible. Then, halfway through the shot, both the fort and the tower disappear. (01:52:20)
Continuity mistake: In one earlyish scene, when Spock and Uhura are in a turbolift, Zoe Saldana has a faint spot on her upper lip that's been covered up. In scenes following, there's no sign of it.
Continuity mistake: When the turbolift carrying Kirk and Uhura arrives at the bridge, Kirk's arms are folded across his chest. In the next shot, Kirk's arms are at his side.
Continuity mistake: When the 72 torpedoes explode in the cargo bay of the USS Vengeance, watch the explosion. The ship's starboard warp nacelle explodes in the close-up. When the shot changes to the wide shot, both nacelles are still intact.
Continuity mistake: When Kirk and Uhura's turbolift arrives at the bridge, Sulu is visible in the background sitting at the helm station at the front of the bridge. As Kirk is walking to Chekov, Sulu then passes Kirk from the opposite side of the bridge, walking to the helm.
Continuity mistake: Near the end of the movie, Spock, with a phaser in his right hand, is chasing Kahn across the urban landscape. Kahn jumps onto a departing garbage scow and with a mighty leap, Spock jumps towards the bottom of the scow and is then shown holding on with two (empty) hands. A moment later, he is shown climbing onto the deck of the vessel, with the phaser back in his hand. Kahn kicks the phaser away and it disappears once again, this time over the side.
Continuity mistake: On Kronos, Harrison's hair is long enough to reach his jawline, but in the brig it's short and neatly coiffed.
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.