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 mike can be seen moving quickly above and to the left of his head.
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.