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.
Factual error: At one point Khan threatens to target the Enterprise's life support systems which are located behind her "aft nacelle". The Enterprise doesn't have an aft nacelle; as the many exterior shots show, it has a port nacelle and a starboard nacelle. Khan a) is familiar enough with Starfleet ships to know this basic fact about the Enterprise, and b) can see its nacelles for himself on his own viewscreen while he's delivering this line. There is no "nacelle" housing the impulse engines. They are enclosed by the hull of the saucer section. (01:37:25)
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)
Factual error: During the Vengeance's fall to Earth, just after hitting Alcatraz, the saucer section hits the surface of San Francisco Bay, the outer rim diving dozens of meters into the water and its rear lifting up almost vertically into the air. A few seconds later the ship is seen from the onshore view, and it is straight and level and heading directly at Star Fleet Headquarters. Hitting the water at that angle and speed, so close to the shore, the ship could not have righted itself and gotten on that trajectory going that fast. It should have sunk or flipped over when it hit the water. Even if it could flip 360°, there was not enough time, distance, or height for the ship to continue on to its target at that speed. The water's drag would have slowed it too much. (01:52:40)
Suggested correction: Maybe the ship's systems are trying to correct its course.
Factual error: After the USS Vengeance blasts the USS Enterprise out of Warp, Sulu says that they are 237,000km away from Earth, but the Moon is between both ships and Earth. Earth's Moon is about 380,000km away from our planet, so the Moon should have been way behind the combatants.
Factual error: Enterprise and Vengeance come out of warp near the moon, 237,000km from Earth. Due to their altercation. They lose power and proceed to fall freely toward Earth. The scene plays as though it takes a matter of a few minutes, too fast to get the situation under control. At that distance, the gravity acceleration from Earth would only be .01 m/sec/sec. This means that they should have had approximately 2.52 days before crashing, especially given their apparent relative stop as per the visible moon.
Plot hole: During the warp-speed chase, the Vengeance literally blasts the Enterprise to pieces, and dozens if not scores of Enterprise crew members are killed and injured in the carnage. The medical crew, including Chief Medical Officer McCoy, should have been working feverishly on the wounded and dying for hours, at least. Instead, as Kirk asks Khan for help, the Sickbay is practically deserted, and McCoy is almost idly conducting blood experiments on a dead tribble. There's no sense of a catastrophic medical emergency whatsoever. It's as though the Sickbay sequence was shot for a different script in which there was no emergency, and then lazily inserted into a rewritten script.
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.
Revealing mistake: When Khan and Spock are fighting on the garbage scow as it glides over San Francisco, you can easily see Spock's stunt double being beaten by Khan's stunt double. And vice versa.
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.
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.
Continuity mistake: On Kronos, Harrison's hair is long enough to reach his jawline, but in the brig it's short and neatly coiffed.
