Operation -- Annihilate! - S1-E30
Revealing mistake: While Spock and Kirk discuss the phaser resistant creatures, Kirk declares that it may be a trap and to move out. When one of the flying parasitic creatures attacks Spock, in his first closeup just as Spock turns around we can see the thin wire leading from the creature to the right side of the screen, and the wire also casts a shadow on Spock's uniform. (00:18:10)
Operation -- Annihilate! - S1-E30
Visible crew/equipment: When Spock and McCoy walk into Kirk's quarters, in the wideshot the white tape mark can be seen on the floor under the desk at Spock's feet, before Spock requests permission to beam down to the planet, and can be seen again when Kirk stands up.
Operation -- Annihilate! - S1-E30
Continuity mistake: When they put the satellites in orbit, Sulu announces they are in place. Then Kirk says "Energize" and the next shot shows the helmsman station and Sulu is absent - some guy in a red shirt is there instead. (00:45:30)
Operation -- Annihilate! - S1-E30
Continuity mistake: When Uhura tells Kirk that she's made contact with his private transmitter she's seated at the communications console, with the two overhead screens above her station, beside the turbo lift alcove. Yet after the contact's been broken, when she tells Kirk, "It's impossible at the moment because they stopped broadcasting," in this unusual shot facing Uhura the turbo lift alcove is not behind her - Uhura is actually seated much closer to Spock's station, note the upper section with overhead screens. Then she's properly seated at her station once again.
Operation -- Annihilate! - S1-E30
Revealing mistake: When Kirk and company beam down, the trees are brown. In the next shot, the trees are green. Most probably a different camera lens was used for the shots. (00:07:10)
Operation -- Annihilate! - S1-E30
Visible crew/equipment: When Kirk and the landing party are standing on the transporter pads ready to beam down to planet, the camera pans to the right as the transporter operator stands at the console, and the end of the set is visible with black cables lying on floor. (00:07:15)
Operation -- Annihilate! - S1-E30
Continuity mistake: After Kirk orders Uhura to reestablish contact with Aurelan's transmitter, when Uhura replies that they do not acknowledge her contact signal, Uhura's communications earpiece is not in her ear, but in the next shot it's suddenly back in her ear. (00:06:10)
Answer: Kirk was getting his physical and Dr. McCoy probably turned off communications, because if he hadn't, Kirk would have left and headed straight for the bridge, leaving McCoy irritated.