Revealing mistake: At different points during the Metrons' transmission to the Enterprise, both Kirk and the Gorn pop into the picture a few seconds after the rocky landscape appears. (00:37:00 - 00:37:55)
Continuity mistake: After Kirk tells the Metrons that he won't kill the Gorn, he yells out "you'll have to get your entertainment someplace else." Two seconds later, Kirk turns his head to the side and looks stunned. That look of surprise takes place a full second before the Gorn starts to disappear. (00:45:47)
Continuity mistake: Kirk turns his head and displays a stunned look... a full second before the Gorn even starts to disappear. (00:45:47)
Continuity mistake: After the battle ends, Kirk looks up to the exact spot where the Metron will be standing, way before the Metron even materializes. (00:45:53)
Visible crew/equipment: When the Metron returns Kirk to the Enterprise he reappears on the bridge, and the actors' chalk marks are visible on the floor where Kirk and crew stand. (00:47:20)
Continuity mistake: When Kirk and Spock are chatting in Kirk's quarters, they finish their discussion and as they head out Kirk orders the ship to red alert. Then after the commercial break, they're on the bridge, the Gorn ship is at a dead halt, and Kirk orders the ship to red alert again. With a hostile ship in the vicinity, Kirk, a highly experienced captain, would hardly have taken the ship off red alert.
Revealing mistake: As Kirk and the Gorn battle, they briefly confront each other from opposite sides of a dead tree which has truncated limbs. One of the larger tree limbs on this supposedly uninhabited, tiny world has obviously been cut off with a chain saw or similar cutting instrument.
Tomorrow is Yesterday - S1-E20
Visible crew/equipment: As Spock gives his report to Kirk on the bridge, the shadow of the boom mic is over his right shoulder. (00:03:35)
Tomorrow is Yesterday - S1-E20
Character mistake: When first considering the impact of Captain Christopher's removal from this time, Spock makes a mistake in his dialogue. He says "They show no record of any irrelevent contribution..." when it should be "relevent..." (00:13:50)
Tomorrow is Yesterday - S1-E20
Factual error: Towards the end of the show the Enterprise is leaving Earth orbit and heading towards the sun. We see the Earth diminish and the moon appear looking exactly as it does from Earth. From this angle we should be seeing the "dark side" of the moon, which looks completely different. (00:40:50)
Tomorrow is Yesterday - S1-E20
Revealing mistake: Traveling towards the Sun and away from the Earth, parts of the Enterprise are missing due to superimposing the model into the current shot. As the Enterprise goes by, one of the warp engines seems to be disintegrating at the rear. (00:42:05)
Tomorrow is Yesterday - S1-E20
Continuity mistake: When Kirk and Sulu enter the records room, they pick the lock. Later when they beam the officer back down, he enters the room without unlocking the door. The room should be locked since they beamed him down in the "past" erasing their having been on Earth and in the records room.
Tomorrow is Yesterday - S1-E20
Other mistake: In the end credits the character of Captain Christopher is credited as Major Christopher.
Tomorrow is Yesterday - S1-E20
Plot hole: In the transporter room the captain calls to see if Major Christopher is ready, Christopher somehow knows exactly what button to press on the console to answer back.
Tomorrow is Yesterday - S1-E20
Character mistake: Kirk introduces Spock as "Lieutenant Commander Spock," but Spock is obviously wearing full commander's stripes on his uniform.
Tomorrow is Yesterday - S1-E20
Other mistake: The Air Force police officer (played by Hal Lynch) was beamed up from inside the records room (after finding Kirk exiting the dark-room) but was returned outside the room... so he was physically transported INTO himself (as opposed to replacing the beamed-up future version at the exact moment and place he was removed as they did the pilot, Christopher).
Tomorrow is Yesterday - S1-E20
Revealing mistake: As the camera looks at the pilot in the cockpit, there are supports on either side of and behind him as well as no clouds where there should be, showing he is on a sound stage set.
Tomorrow is Yesterday - S1-E20
Continuity mistake: When the plane is coming up to intercept the Enterprise, it's shown flying through thin clouds, yet when inside the cockpit, there are no clouds to be seen.
Tomorrow is Yesterday - S1-E20
Visible crew/equipment: When Kirk hears the audio for the first manned moon shot, he gets up to walk over to Spock. As the camera pans to follow, the shadow of the boom mic can be seen moving quickly above and to the left of his head.
Factual error: When they are searching for Finney hidden somewhere in the ship, all ship noises are deadened, and the heartbeats of those on the bridge are muffled by McCoy. In order to locate Finney's heartbeat the ship's auditory sensors are magnified by "one to the fourth power". That's 1x1x1x1 = 1, ie no magnification.
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.