Sarek has great influence with the Federation. It would have been a great help to Kirk and McCoy if he had explained to Federation what was wrong with the doctor. He would probably have no trouble asking Federation Command to have Grissom recover Spock's body and take it to Vulcan. Then Sarek, Kirk and McCoy could have flown to Volcan from Earth and performed the ceremony without incident.
When Kirk & Co are stealing the Enterprise, both Kirk on the Enterprise and Captain Esteban on the Excelsior give the order for '1/4 impulse power' while still in the enclosed space dock. This is incorrect. Inside space dock the order would be for thrusters, not impulse engines. 1/4 impulse power would mean they are traveling at 1/4 the speed of light. While slow by intergalactic standards it would be far too fast for space dock, especially an enclosed one. Thrusters are used for slow speed maneuvering.
In the previous film, when the Enterprise approaches the Reliant and receives no reply to her hails, Saavik begins quoting General Order 12; "On the approach of any vessel, when communications have not been established... ". Kirk ignores her - and the regulation - and as a result the Enterprise is badly damaged and members of the crew are killed.
He should therefore not have made the same mistake when approaching the Genesis planet and receiving no reply from the Grissom. As a result the Enterprise is badly damaged - again!
In addition, as well as the charges brought against the crew as listed in Star Trek IV, Kirk should also have been charged with negligence leading to the death of crew, and disregarding a Starfleet General Order - twice.
When Kirk surprises the Klingon Maltz, we see Maltz with crossed arms and holding a disruptor pistol as he turns toward the door. He pivots 180 degrees, so his original position would have been facing the captain's chair. The Enterprise officers are on his right, which is not too unrealistic, but as Kirk enters with phaser drawn, we catch a glimpse of Chekov disarming Maltz, and his positioning is opposite the other officers across the room. Separating prisoners like that would not be a safe procedure. They should have all been standing together.
The USS Enterprise had more damage markings on the hull at the start of this film then it did at the end of Star Trek II: The Wrath of Khan.
Considering that this film was set immediately after the events of The Wrath of Khan, there is no explanation as to why these mysterious markings appear on the Enterprise. There were three markings on the hull at the end of the previous film, one to the star drive section, one to the neck section, and one to the underside of the saucer section. In this film the star drive section and warp engines are most notable for the mysterious damage.
When Valkris, the Klingon spy, first approaches the freighter captain from behind, we can only see the bottom portion of her torso. We cannot see her face, but there definitely is something covering her front. However, when we see her face in the next shot, her face and torso are uncovered.
On his beam down to the Genesis planet, Kirk removes his jacket and tosses it to the ground. When he beams back aboard the ship, he is still without the jacket. When he later exits the ship down the ramp, he is again wearing his red jacket.
At 31:40 Kirk is talking to Admiral Morrow in the bar, and there are no drinks on their table. At 32:22, drinks have magically appeared with no sign of a waitperson or sound of the glasses hitting the table.
When Vulcan High Priestess T'Lar was performing the fal-tor-pan ceremony, and during close-ups, she lays her hand flat on McCoy's forehead. Yet in the wide shots, her hand is in a spider-like position on his face.
The Security Alert screen features a diagram of a Constitution-class vessel from Star Trek The Original Series instead of the refitted version from the movies. Also, the registry on the diagram is NCC-200.
When Kirk inquires to Admiral Morrow about possibly repairing and refitting the Enterprise, Morrow tells Kirk that there is to be no refit because the Enterprise is "over 20 years old" (as of 2285-the year this movie is set). This is an understatement if we consider information established from the Star Trek: The Cage and the Star Trek "Menagerie" 2-parter. Those stories had established that Kirk's 5-year mission with the Enterprise (from 2266-2270) was not the first 5-year mission for that vessel, but in fact the Enterprise had at least 2 previous 5-year missions under then-Captain Christopher Pike from 2251-2262, which would make the Enterprise at least 35 years old and not 20 as Admiral Morrow suggested. This also does not take into account the previous Enterprise missions under Captain Robert April in the 2240s mentioned in Star Trek: The Animated Series the animated series, but this is often disregarded as the animated series is not considered to be part of Star Trek canon. However, it is irrelevant how old the Enterprise is. It could be 35 years old, or 100 years old, the fact remains that all of these dates are technically "over 20 years old."
They totally redid the set for the inside of the turbolifts between this movie and the last one, so the turbolifts look completely different inside, meaning Scotty while attempting to repair the battle damage from the last movie apparently thought it necessary to make drastic changes to the inside of the turbolifts on the way back to space dock.
At the beginning of the pon farr sequence, a tree is uprooted next to Saavik. In a brief shot afterward, the tree can be seen to be falling on a Klingon officer, suggesting the shot may have been taken from a later sequence on the Genesis planet.
In the opening sequence when the Enterprise fires Spock's casket at the Genesis Planet, several stars from the background can be seen through the translucent Genesis Planet image. The planet moves slowly to the right as the shot progresses, and yet the stars bleeding through the image from the background remain stationary.
The goof items below may give away important plot points.
At the end, Sarek asks Kirk "But at what cost? Your ship... your son." As a logical being, Sarek would have known that the Enterprise had already been decommissioned, so Kirk's losing it was not related to rescuing Spock. And Sarek would have known that if Kirk had not gone to Genesis to rescue Spock, then David still would have died, along with both Saavik and Spock - either when the planet exploded, or at the hands of the Klingons. So neither the loss of Kirk's ship, nor his son, were costs that could be attributed to the rescuing of Spock. The real price for Kirk's actions was his career, along with the careers of the others who accompanied him on the mission - a price they all acknowledged, and they felt was worth paying. And since they had no foreknowledge of what would happen when they returned to Earth to face the music, they fully expected to have to pay it.
There is no reason for the Enterprise crew to steal the ship and return to Genesis. When Sarek reveals to Kirk that Spock's Katra is in Dr McCoy, his instruction to Kirk is to return them both to Vulcan. However, this must be referring to Spocks Katra, not his physical body, as at this point in the film neither he nor Kirk has any reason to believe the physical body wasn't destroyed in the photon torpedo coffin (David and Savik were both surprised to find the coffin intact). Kirk doesn't find out about Spock's resurrection until he arrives at Genesis. So surely Kirk should have taken McCoy directly to Vulcan, and could presumably have used a commercial transport to do so. Although Kirk had previously said 'I must return here some day' with reference Genesis, it seems odd to do it as a detour in an urgent mission to save his friends soul, especially as he has to steal the Enterprise and destroy his own career to do so.