Continuity mistake: After Spock talks about Sun Worship on the bridge, Uhura goes to correct him. As she's sitting at her console, her arm is covering the note board. When the angle changes to include her, Kirk, Spock and McCoy, her arm is above the note board. Back to a close up, and her arm's covering it again.
Continuity mistake: When Kirk, Bones and Spock are commanded to stop, and raise their hands, they do so. After a moment, Kirk starts to lower his hands. After the camera cuts to a shot from behind, Kirk's hands are by his sides and he goes for his phaser. After another warning shot, he says "I think he means it." The camera goes back to facing them, and his hands are up again.
Add timeMovie Nut
Character mistake: Spock expresses amazement that the natives of this planet speak Earth English, however, he and Kirk were both on the bridge when Uhura tapped into the planet's news broadcast and already know that they speak Earth English, and there's no reason to tell McCoy, because he heard it too. Commenting on it would be illogical.