Continuity mistake: When Khan's number one officer is dying in the arms of Khan, they exchange a word or two before the first officer dies quite dramatically with his eyes open. Khan then fully embraces the corpse and looks up to the viewer screen and vows to get even with Kirk. However, the "corpse", whose eyes are open, closes them upon Khan's embrace.
Plot hole: Why doesn't Reliant know that Khan is exiled here? The Federation is so terrified and opposed to genetic engineering that it's still illegal 300 years after Khan. So why is there no warning along with the data on the Ceti Alpha system? Kirk logged what happened with Khan and his solution of marooning him. Starships use nav data to navigate star systems. Ceti Alpha 6 exploded, yet the helmsman or computer never noticed that there is one less planet than there was when Kirk was there? There is no debris from the explosion? Ceti Alpha 5 is the exact same size and was conveniently blown into the exact same orbit as Ceti Alpha 6 used to have? So there is nothing whatsoever to make the crew even suspect that it's not 6? Enterprise would have to have scanned the planets in the system to know that one was habitable for Khan. Did Ceti Alpha 6's destruction somehow magically turn Ceti Alpha 5 into its exact duplicate? If Starfleet ships have been there to map after Ceti Alpha 6 exploded, none of them bothered to check on the exiles? Pretty callous for Starfleet, don't you think? With the technology and amounts of information available to Starfleet vessels, there is NO logical reason for the Reliant to think that this planet is Ceti Alpha 6. Finally, would the Federation be willing to test a device whose exact effects will be unknown on a planet so close to another inhabited one?
Revealing mistake: When the Enterprise is leaving space dock, look at the right (starboard) side of the ship. You can see the shape of the mounting arm the model was mounted on, even though it was blacked out to look like space, and it also blocked out the bottom of the dock. The footage was reused from Star Trek: The Motion Picture.
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Continuity mistake: Spock's funeral takes place in Torpedo Bay 1, on the starboard side of the ship. The interior shots, however, show Torpedo Bay 2 (you can see the label and the airlock from the beginning of the movie). In addition, the arm that lowers the torpedo is marked with a '2'. Making matters worse, Torpedo Bay 2 was destroyed in the battle with USS Reliant.
Continuity mistake: When Spock is dying within the glass confines of the ships nuclear power source room with Admiral Kirk (William Shatner) on the opposite side of the glass, in one scene speaking to Spock, Admiral Kirk's red Federation uniform jacket lapel is unbuttoned at the top. In the very next scene the uniform jacket is buttoned.
Continuity mistake: When Reliant is hit, a large piece of debris falls to the deck, killing Joachim. In the wide shot as Khan makes his way to the debris, a large mass of hanging wires dangles from the ceiling, lower than Khan's head while he is bent over. But the next closer shot has Khan standing erect, lifting the debris, and the wires have vanished. (DVD Director's Cut).
Audio problem: When Kirk says, "Stop energizers," watch his lips closely - he really says, "Stop engines." Mike Okuda points this out in the text commentary on the Director's Edition DVD. The reason the line (and also the one following it) was redubbed was because someone pointed out during post-production that the engines couldn't simply be stopped on a dime.
Character mistake: While Khan is "interviewing" Chekhov and Terrell, he stated, "On Earth, two hundred years ago, I was a prince, with power over millions." The official date for this movie is 2285. That would place Khan on earth around 2085 by this statement. However, it is made clear in the episode "Space Seed" that Khan and his followers escaped earth in the year 1996: nearly one hundred years earlier. Quite a way off to be a rounding error.
Continuity mistake: When Spock gives the neck-pinch to McCoy, who slumps to the floor slowly, the floor inside the chamber is a dark-tan/light-brown color, but the close-up of the mind-meld on McCoy's face shows the same floor lit prominently with blue lights. (Director's Cut DVD).
Continuity mistake: After being marooned inside Regula I, McCoy is tending to Chekov who is lying unconscious. He says, "He's coming around." You then see McCoy handing him a bandage to hold to his ear and Chekov raises his arm to hold it. Immediately following, there is a shot of McCoy saying "...She's finished," (referring to the Enterprise) and you can see Chekov raising his hand to his ear again.
Continuity mistake: After the Reliant attack, when Scotty's nephew is talking to Kirk in sickbay, he asks Kirk if the word is given, and Kirk takes his bloody hand then places it against his tunic. After he dies, the next scene shows the bloody handprint in a totally different spot on the tunic.
Continuity mistake: When McCoy bumps into a hanging body's arm and yells 'Jim.', the next shot shows Kirk lowering a body from an upper level by rope. To his right, another body dangles (feet point up, frontside visible). In the following close-ups of Kirk, this body is much closer to him and is turned over (feet point down, backside visible). No time compression occurs between the two shots. (Director's cut DVD).
Continuity mistake: When Spock is kneeling in his quarters, talking with Kirk, a shot facing Spock's front shows that the bottom of the lighted mirror on the wall is behind his head. In the next side shot, it's not there as he is now much further from the wall and the mirror is out of the shot at right. The angle of the second shot does not excuse the mistake- the mirror should still be visible at the new angle. (Director's Cut DVD).
Continuity mistake: When Engineering is taking damage and the trainees are fleeing, Scotty's nephew goes to the aid of an injured crew member. A containment bulkhead is lowering to seal the compartment as he approaches it and as the shot ends, the bottom of the door has reached the lowest edge of the round collar at the left of the screen. Moments later, the actual rescue is shown while the door is lowering through the same area as before- having started higher than it was when the prior shot ended. The change in camera angle is not creating an optical illusion. (Director's Cut DVD).
Continuity mistake: The Enterprise is (slowly) attempting to put distance between herself and Reliant (which is about to explode). Whenever Enterprise is shown coming toward camera (or watching Reliant on its viewscreen), Reliant is alternately seen from its starboard side pointing at our 2 o'clock position, from port/aft listing hard to starboard, from it's aft/top area, pointing toward 1 o'clock, and from starboard/bow pointing to 5 o'clock... yet Reliant isn't wobbling or moving, and Enterprise maintains a straight (shortest) course away from her... all suggesting Enterprise is traveling in four directions at the same time. (Director's cut DVD).
Factual error: Inside the nebula, the Enterprise rises from below and fires a photon torpedo at the Reliant, striking it directly on the dorsal torpedo pod. Watch as the torpedo hits and the pod explodes. Large pieces of the bulkhead explode outward, then begin to fall downward towards the saucer section before they cut camera angles, despite there being nothing dragging them in that direction.
Continuity mistake: When Kirk and McCoy are in the turbolift, just before Kirk is told about the message from Carol Marcus, they are both standing right next to the door, but in the close up of McCoy, right after Kirk is informed of the message, McCoy has suddenly moved along the wall.
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Continuity mistake: When the Enterprise leaves spacedock, Saavik orders 'half impulse'. However, in the exterior shots the impulse engines are not lit. The reason is that ST II uses stock footage from ST I for the spacedock scene. In that movie, the ship leaves the dock using thrusters. The obvious give away is the blue deflector from ST II forward, while ST I had a red deflector. It is a short scene less than 2 seconds, you really have to watch for it. The thrusters are on, as seen in the parts of the scene with the blue deflector, and suddenly they are off and the deflector is red for a few seconds.
Other mistake: When Captain Terrell shoots himself with the phaser, the phaser disintegrates along with his body, when it should have just dropped to the ground (as often shown in the various Trek TV shows). It wouldn't make sense to explain that the phaser disintegrated because Terrell was touching it, because then it would be impossible to explain why nothing happens to the ground that people are standing on when they get shot (Director's Cut).
Continuity mistake: In the scene when Khan first opens fire on the Enterprise, the exterior shots show the damage on the forward part of the engineering hull. However, the damage on the interior shots is occurring on the aft section. Which is to say if the exterior and interior damage lined up the way they're supposed to, Scotty and his cadet engineers would've all been killed in a warp core breach.
Revealing mistake: When Chekhov and Terrell see the Ceti Eels moving around in the tank for the first time, it's obvious that it's not sand in the tank. As the creatures move underneath, all the 'grains' move in unison, and not a single grain of sand is disturbed nor do they tumble over one another.
Plot hole: Khan said that the crew of the Botany Bay had been stranded on Ceti Alpha VI for 15 years. Considering that most of his crew were in their 20s, wouldn't that mean they were all children when they were first stranded? In the original TV series, all of these superhumans were already adults, so how come Khan was the only person to age?
Continuity mistake: After the reliant explodes and the Enterprise is safe, Kirk goes to engineering to see Spock in the radiation filled chamber. During this entire scene, Kirk's tunic is open as Scotty and McCoy keep him from entering the chamber. As Kirk approaches the chamber to talk to Spock, the tunic is partially closed. The next shot shows the tunic all the way open as Spock walks towards Kirk.
Other mistake: After the Enterprise blows the port nacelle off the Reliant, the destroyed Reliant bridge is shown. The three sheaves of wires hanging from the ceiling should be on a tilt with the angle of the ship rather than straight down. Even accounting for the artificial gravity unit, which could have been damaged.
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Continuity mistake: When the Enterprise is making a run for the Mutara Nebula, they show a scene in a photon torpedo bay. On the wall the sign says "TORP BAY 4." The problem is that the Enterprise only has 2 photon torpedo bays. Bay 1 (Starboard side) and Bay 2 (Port side). This version of the Enterprise has no aft photon torpedo bays.
Continuity mistake: When Admiral Kirk and party arrive in the transport pod, they dock on the port side docking port in the secondary hull. But the airlock they emerge from is in the docking port for the port side torpedo bay, as signified by the sign in the background saying "TORP BAY 2." You can see the docking port they are supposed to have docked at to emerge from on the side of the torpedo launchers, just above of the secondary hull. The reason for this is because they re-used the stock footage from ST:TMP when Kirk and Scotty docked at the same docking port.