Continuity mistake: The blood stain on Kirk's jacket keeps moving around.
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. (01:29:05)
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. (01:43:20 - 01:44:45)
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. (01:40:10)
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). (01:28:20)
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. (01:14:05)
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). (01:35:40)
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). (01:03:55)
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. (00:58:20)
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.
Continuity mistake: When Scotty's nephew dies in Sick Bay, McCoy is holding him up a bit. The wide shot shows Mccoy's thumb is up near the young man's ear, but close-ups of the boy show the thumb isn't there because McCoy's hand is lower on his back. (Director's Cut DVD). (00:58:15)
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). (00:39:30)
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). (00:50:35)
Continuity mistake: In the Kobayashi Maru, Dr.McCoy is knocked to the deck unconscious, his head on a support; next shot shows McCoy's head lying on Sulu's leg; next shot shows McCoy's head back on the bare deck.
Continuity mistake: In the training simulator at the beginning of the film, after Sulu and McCoy have both fallen, McCoy has his head resting on Sulu's hip at first. Then, in the next shot, his head is resting closer to Sulu's knee. (00:05:50)
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). (01:36:50)
Continuity mistake: In the Genesis cave, Kirk puts on his glasses to look at his watch. In the very next shot, he is not wearing his glasses. (01:15:20)
Continuity mistake: When Kirk is marooned by Khan, Carol asks David to show them the Genesis Cave and he says "we can't just sit here", Kirk puts on his glasses, looks at his watch and replies "yes we can", in the very next shot the glasses are gone as David stands up.
Continuity mistake: When the Enterprise leaves spacedock, Saavik orders 'one quarter impulse power'. 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.
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. (00:50:15)
Chosen answer: I imagine there was a memorial service for everyone killed. Starfleet's policy on corpses is probably to return them to Starfleet HQ where their families can collect them for whatever services or ceremonies they want unless the crewman had left instructions specifying otherwise. There's no telling why Kirk sent Spock's body to Genesis. Based on Sarek's reactions in ST3 he almost certainly went against Spock's wishes, unless of course, Spock left no recorded instructions and Kirk did what he thought would please Spock based on his being highest ranking officer and Spock's closest friend. It also seems very out of character for Spock to just assume that whoever he transferred his katra to would be able to handle it and carry out his wishes (McCoy certainly couldn't!). Ultimately it seems we have to chalk it up to a plot device to base the sequel on.
Grumpy Scot
According to the novelization, Kirk's intentions were to send Spock's remains into the Genesis sun. Lieutenant Saavik altered the trajectory of the torpedo beforehand, due to Spock's desire to see the Genesis effect for himself. The torpedo casing was expected to incinerate when entering the atmosphere. As pointed out by David Marcus in STIII when the pod was detected on the scanners, the gravitational fields were in flux at the time, and the pod had obviously soft-landed on the surface.