Revealing mistake: In McCoy's video of the Capellans, the weapon thrown at the sapling actually misses it and nails a nearby bush instead. The tree, however, obediently breaks in half and falls over anyway. (00:00:20)
Deliberate mistake: When the decoyed Enterprise heads back to Capella, the special effects shot is reversed to indicate that it's going back in the other direction. Unfortunately, this gives us two brief shots of the ship with the registration numbers backwards. (00:37:40)
Continuity mistake: Mr. Sulu's equipment comes up to aid him at red alert, yet shortly after it is gone. (00:39:00 - 00:40:00)
Continuity mistake: Kirk's arrow strikes the Klingon in the knee. But a few shots later, the shaft is protruding from his thigh, several inches above its original position. Still later, he's holding one hand to his calf just below the knee, which isn't where the arrow was either time. (00:43:40)
Continuity mistake: When Kirk's arrow hits Kras it protrudes from his leg, but in the next wideshot as Kras screams and stumbles the arrow is quite gone from his leg, but three shots later the arrow is back in his leg while he tries to pull it out. (00:43:40)
Visible crew/equipment: After Kirk hits Kras with an arrow Spock's arrow hits a Capellan on the cliff, and when the Capellan falls into the bush, a crew member wearing sunglasses and a white T-shirt is visible at the left side of the screen. (00:43:50)
Continuity mistake: After Maab gives Eleen back her life and forfeits his own life, when Keel throws the kleegat and hits Kras he drops the phaser in the closeup, but in the next long shot the phaser is back up in the Klingon's (stuntman) right hand. (00:45:50)
Continuity mistake: When the Klingon shoots Maab with a hand phaser, the beam is yellow as he fires, but red when it strikes Maab. (00:46:00)
Continuity mistake: The Klingon is standing on a hillside above Maab, yet when he fires his phaser, the beam streaks upward. From that angle, he wouldn't have hit anything but sky. Nevertheless, the beam somehow re-angles itself downward so that it hits and kills Maab. (00:46:05)
Continuity mistake: Before the Capellans reach him, the Klingon's body moves into a completely different position, and to a different spot on the ground, than it was in when he first fell. (00:46:10)
Continuity mistake: During the coup attempt, one Capellan fights with the leader and gets stabbed. Before and after he is stabbed, the man's outfit changes entirely (look at the fur scarf, which goes from purple to orange.) His costume also changes color.
Continuity mistake: In a wide shot of the Capellons and the Klingon walking down the hill, the Klingon trips and falls to the ground and picks himself up. Next shot, tight group with Klingon, he is suddenly brushing off his pants.
Suggested correction: After Kras falls, the next shot you see him still on the ground and starting to stand up, although Maab blocks the view of him. The shot cuts to the rocks and then when it cuts back, you see Kras walk up and stand next to Maab, then he starts to dust himself off.
Suggested correction: Why would he not be doing that in the next shot? There is no continuity issue.
Revealing mistake: In the tent after Kirk and friends give up their weapons, there is a small fire in the holder in the center of the room. Although the flames are slightly off center to the camera's left, the are projections of flame light from off the camera's right offscreen.
Revealing mistake: When the delegation of locals approach Kirk's party, the Red-shirt yells "KLINGON!" and goes to fire. As he moves, you can see the outline of the block the alien weapon will stick in.