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.
Arrangement of Kirk's duelling pistols on the wall in the background when Sarek and Kirk are talking in Kirk's home.
The display for Sector 3 on Saavik's screen first shows LIFEFORM blinking above the ground display and with data on the left. Next shot shows no data on the left but LIFEFORM is blinking below the ground display. It changes back on a subsequent shot.
The direction the Bird-of-Prey is turning as it opens fire on the cargo ship.
Phase of the Earth's Moon when the Enterprise arrives at space dock after the battle with Khan, and when Kirk steals the Enterprise.
As the Grissom discovers Spock's tube on the planet, the display for sector 3 misspells Celsius as Celcius, although the other 2 displays are correct.
The security alert screen features a diagram of a Constitution-class vessel from Star Trek (1966) instead of the refitted version from the movies. Also, the registry on the diagram is NCC-200.
When Savik berates David about using proto-matter, she talks about all the people who died because of his choice.
The use of proto matter had no impact on any event up to that point. That choice did not cause any deaths.
Some fans have noted how the security detail, while the Enterprise is docking after the encounter with Khan, carry phaser pistols that are different from the ones seen in the previous film. It can be argued that Starfleet vessels are stocked with different styles of phasers, and that the ones seen in this film were just never used previously.
During the battle with the Klingons, Scotty admits that he didn't expect them to go into battle. Though one could assume that a seasoned Starfleet officer who has faced all kinds of situations that change from moment to moment should have been prepared for all possibilities including going into battle, it is understandable why Scotty only prepped the ship to bring them to the Genesis planet. A battle with a Klingon ship would not have remotely been something to expect.
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.
When Kirk and Kruge are fighting, a piece of the cliff breaks away and wiggles down the side of the cliff rather than falling like a rock.
Allan Miller's facial prosthesis never fits quite right. His human lips can easily be seen whenever he talks.
Obvious stunt doubles during the fight between Kirk and Kruge 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 monitors on the Enterprise bridge are round and cut off messages displayed upon them.
When the sun sets on Genesis there is what appears to be moonlight providing illumination. But Genesis is a new planet and does not have any moons. So there should not be any light once the sun is down. Obviously this is studio lighting so that the audience can see the actors.
When Saavik confronts Marcus, trowel marks are clearly visible in the plaster of the "cactus" behind them.
During the self-destruction of the Enterprise, there's an explosion where a Klingon goes flying over the navigation console. When he lands, an arm can be seen helping him.
The very last scene, a Vulcan lady next to Sarek is seen smiling.