Visible crew/equipment: After Spock asks Scotty if there's enough battery power to electrify the exterior of the ship, Spock tells everyone, "Get to the center of the ship. Don't touch the plates. Be sure you're insulated," and just as Spock turns in the rear compartment we can see the edge of the shuttlecraft set behind Spock.
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Continuity mistake: After Spock tells Boma and Gaetano that he's in command and they should fire only to frighten, not to kill, one of the creatures throws a spear and then his shield at the trio, and when the shield hits the ground it's much smaller than the huge shield lying on the ground in the next close-up.
Continuity mistake: While Kirk questions Spock about his command decision on the Galileo, shots of Uhura and Mears show the ladies close together at Uhura's station with Mears' hands hidden but close up shots of McCoy show Mears and Uhura in the background further apart from each other and Mears' hands in front of her body.
Continuity mistake: In the first scene when Spock is piloting the shuttle craft out of the Enterprise and into space, as the bay doors open you can see both the ship's shuttles, the Galileo, and right behind it the Columbus. Yet as soon as the Galileo clears the bay doors, in the immediate reverse shot, the bay is empty and the Columbus has disappeared.
Character mistake: In the scene when the shuttle is finally repaired and lifting off the planet, Spock asks "Fuel status?" and Scotty incorrectly answers "15 pounds PSI, sir. Approximately enough for one orbit." The correct answer would be simply "15 PSI" without the redundancy, as the P in PSI already signifies pounds. As an engineer Scotty would know this.