Goofs

During the docking with the Enterprise, shuttle control gives them permission to dock at the torpedo launching bay. Instead, the shuttle is clearly shown to dock near main engineering. In addition, Kirk and the others clearly board the ship through the torpedo bay. The shuttlepod docking sequence, as well as additional visuals of Enterprise in and departing from drydock, are reused footage from Star Trek: The Motion Picture (1979).

After David Marcus says "We can't just sit here," Admiral Kirk puts on his glasses and checks his watch, saying "Oh, yes we can." In the very next shot, the glasses are gone.

Several monitors on the bridge of the USS Reliant show ship diagrams that don't match the actual shape of the ship as we see it elsewhere in the movie - a result of the bridge set being used for both the Reliant and the Enterprise. Indeed, at least one of the diagrams is for a third design.

The footage of the Enterprise leaving dry dock shows an arboretum on the port side of the ship. This is absent from the ship for the rest of the film, as the dry dock footage was reused from Star Trek: The Motion Picture (1979).

The position of the chest flap on Admiral Kirk's uniform changes from being flipped open between the moment McCoy and Scotty hold him back to almost closed when he approaches the radiation-filled chamber a few steps away.

When the Enterprise approaches the Reliant for the first time and each ship drop speeds to one-half impulse power, the stars can be seen moving in the background at a rate much faster than the Starships are traveling towards each other. The stars should appear motionless when the two ships are shown approaching each other in the same scene.

Kirk's eulogy for Spock says he gave his life to "protect and nourish" a new world, but his actions to fix the warp drive only saved the lives of the Enterprise crew, and the Genesis wave would've transformed the planet regardless of whether they were caught in its wake or not.

When the Enterprise enters the Matura Nebula it is depicted as a cosmic mist with occasional lightning storms. But lightning storms do not exist in space.

Chekov and Khan recall having met each other. Although Chekov was not a bridge officer when Khan came on the Enterprise in Space Seed (1967), it should be remembered that when Khan first took over Enterprise, he started with the engineering deck. Chekov was engineering ensign at the time, and mounted resistance against Khan, according to the movie's novelization. Surprisingly, Sulu was also absent from Space Seed, a point which no one ever brings up.

Saavik, a female, is referred to as "Mr. Saavik". In the Trek universe, Starfleet Officers are referred to as Mister, regardless of sex or gender. This is true even in today's modern U.S. Navy.

Kirk never reminds Khan that he did not maroon him and his followers on a hostile planet. Khan freely accepted exile there rather than go to prison for attempting to take over the Enterprise. He was grateful to Kirk to be given the choice.

Khan clearly states that he is not angry at Kirk for leaving him on Ceti Alpha V, it is because no one from Starfleet ever came back to check up on him and his followers to see that they were making out okay.

In Space Seed (1967), Khan was marooned on Ceti Alpha V with a few dozen of his followers, all of whom were about his same age (roughly their mid-thirties). Now in the movie, set fifteen years later, Khan has aged, but he's surrounded by followers who are all appear to be in their twenties; they're too young to have been the disciples with him in the original episode, but too old to have been born on the planet.

In the original series "Space Seed" episode, they discuss how Khan and his followers are genetically engineered. Perhaps, their aging (or apparent lack thereof) is part of that genetic engineering.

The Kobayashi Maru simulator is a failure in logic. Every cadet in the academy knows about the simulation and that it is a no-win simulation. There is no challenge, nothing is learned because there is nothing to lose.

The scenario allows for many different reactions by cadets to the no-win situation. It is designed to test their mettle, whether they make a brave attempt to rescue the stranded vessel despite it being in the Neutral Zone, whether they stand by and nothing, etc.

When Chekov steps out of the Botany Bay into a blinding sandstorm and sees the robed survivors, their robes are resting still - there is no wind around them. This may have been a deliberate artistic choice on the filmmakers' part.

In one shot on the Reliant bridge, when the turbolift doors are open, a ship diagram for the Enterprise can be seen inside the lift. This is because the same set was used for both bridges.

In the computer image of the Genesis probe approaching the planet, the camera is about to collide with a mountain when a narrow canyon blinks into existence to let it through.

There is a "No Smoking" sign on the bridge of the Kobayashi Maru simulator. This clearly appears onscreen during the early part of the scene. Gene Roddenberry had them removed but not until some footage had already been filmed.

Wires are visible attached to Chekov's uniform when Khan lifts him up with one hand.

When Spock does the neck pinch on Bones, he takes the gloves from Scotty who is unconscious, then goes in to the reactor chamber. Both Bones and Scotty suddenly wake up and start yelling at Spock.

When Scotty and McCoy are yelling at Spock not to open the main energizer, Scotty's and McCoy's mouths are not moving in sync with the words being spoken.

When Spock and Saavik are speaking Vulcan, their mouths are speaking English.

When the debris falls on Joachim.

While the Enterprise is flying towards the Mutara Nebula, Torpedo Bay 4 is shown being loaded. The Enterprise has only two forward-facing torpedo bays.

The Reliant chooses a planet in the Ceti Alpha system and yet no one acknowledges the stranding of Khan there a little over two decades earlier. The computer, whose memory should be infallible, does not note the events of decades earlier when it scans the system in advance of the Genesis test.

When the Reliant scans for life forms, why couldn't they detect Khan's people? The discussion on the Reliant implies that the only thing they are detecting is a minor life sign that is ambiguous for it to even be a life form (hence beaming down to investigate). Even the hand scanners that Terrell and Chekov carry just detect "Khan's pets" in the glass cases, and not the people outside.

After Kirk hears the jammed transmission from Carol Marcus, Spock tells him they are 12 hours away from Regula at present speed. Immediately afterward, they view the Project Genesis video and are attacked by Khan in the stolen Reliant. The warp drive is damaged in the battle, yet they manage to get to Regula a short time later anyway.

When McCoy gives Kirk the bottle of Romulan ale, he reads "2283". Aside from that the bottle doesn't have any apparent writing and should be in Romulan, Kirk has difficulty reading without corrective lenses, which McCoy later gives him.

When Khan first meets Terrell and Chekov, he tells them that "200 years ago on Earth, I was a prince," and "these people have sworn to live and die at my command 200 years ago." The movie, however, is set in the year 2285, and Khan started his explanation by saying that the Botany Bay launched in 1996 - three hundred years ago.

Several characters mention that because he reprogrammed the computer, allowing him to defeat the Kobayashi Maru test, Kirk has never faced a no-win situation, including the Admiral himself. However, Kirk only reprogrammed the Kobayashi Maru test the third time that he took the test, so he faced the no-win scenario twice before.

Saavik expresses her surprise that Spock lied, yet when she quotes Rule 15 so that she could accompany the Admiral to the Station, Kirk replies, "There's no such rule."

Kirk slightly misquotes the final sentence of "A Tale of Two Cities" by Charles Dickens: "It is a far, far better thing that I do, than I have ever done; it is a far, far better rest that I go to than I have ever known."