Revealing mistake: A straight and level seam connecting the top and bottom halves of the tunnel Spock is crawling through is visible.
Suggested correction: Views of the tunnels made before the creature was wounded by Kirk and Spock appear almost perfectly smooth. It is explained that the creature exudes a powerful acid to dissolve the rock. This tunnel was made after the creature was wounded, so it is logical that the wounded portion of the creature would secrete less acid thus leaving an imperfection as the creature tunnels. This could be a case of incredible attention to detail by the set designer rather than an error revealed.
This correction is too much of a stretch to explain a perfect seam by the wounded Horta. Plus, if the Horta was secreting less corrosive substance, then that area would be less eroded, not more. If attention to detail was paid, then the area would have an outward seam, not an inward one.
Character mistake: Lt. Joey said to Lt. Sulu "You don't outrank me and you don't have pointed ears" but Joey is a junior grade lieutenant so Sulu would outrank him.
Where No Man Has Gone Before - S1-E4
Continuity mistake: When Kirk is fighting Gary Mitchell, his tombstone reads James R. Kirk. Kirk's middle name is Tiberius. Mitchell is a friend of long standing and would not have got it wrong. (00:44:30)
The City on the Edge of Forever - S1-E29
Factual error: Edith Keeler says to McCoy, "My young man is taking me to see a Clark Gable movie." In 1930, Clark Gable was an uncredited bit player who had last made a film in 1926 - Edith, a New York charity worker, would not even have encountered his name.
Revealing mistake: As the bridge crew monitors Psi 2000 on the view screen, a glitch in the special effects matte makes the planet vanish briefly and then reappear - twice. (00:12:30)
Revealing mistake: When the laser cannon starts firing at the Talosian rockface, a styrofoam block falls and rolls away on the left side of the screen. After a brief shot of the crew, we see the cannon still firing, and the exact same block falls and rolls off screen on the left again. (00:30:15)
Mudd's Women - S1-E7
Continuity mistake: As the women are beaming aboard in the transporter room, McCoy's uniform switches from the standard blue tunic to his short-sleeved medical smock and back again between shots. (00:05:55)
The Man Trap - S1-E2
Continuity mistake: When Rand brings Sulu the plate of food, it has a bowl of colored cubes on it. Then there's a cut to a close-up of Sulu eating the cubes when Green is staring at it, and the bowl is now a plate. Then in the long shot it's a bowl again. (00:24:22)
Other mistake: Spock and McCoy have a brief argument over whether Charlie could have survived on his own all those years. Because they're talking at the same time, Spock saying "Doctor" as McCoy says "Mr. Spock," the closed captioner apparently misunderstood McCoy's line. The caption has him calling Spock "Dr. Spock." (00:09:15)
Where No Man Has Gone Before - S1-E4
Visible crew/equipment: When Dr. Dehner is talking to Gary Mitchell in sick bay, when he grabs her arm you can see the shadow of the boom mic on the door and adjacent wall. (00:19:25)
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.
Revealing mistake: In the first illusion, Vina runs down the path from the fortress to Pike. When we cut to close-ups, they're both suddenly standing much closer to the building than before, and the fortress has changed color from brownish orange to white. (00:23:50)
Continuity mistake: Initially, the Enterprise orbits Psi 2000 as the planet turns westward. But in later shots, on the bridge view screen, the planet has reversed directions and now turns eastward. (00:04:05 - 00:12:00)
What Are Little Girls Made Of? - S1-E8
Continuity mistake: When the android Kirk boards the Enterprise and takes a "command pack," he walks out and down to the transporter, but he doesn't have the pack in his hand.
Continuity mistake: When Kirk is facing the Horta he has his phaser in his right hand when seen from the front but when seen from behind he has his communicator in his left hand and no phaser. (00:31:00 - 00:38:00)
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.
Other mistake: Spock records a log entry as the "second officer". It appears they got "first officer" confused with "second in command." (00:36:15)
Revealing mistake: Due to a poor edit, there's an odd jump cut and a change of lighting just as the Keeper comes out of the elevator on his way to an attempt to steal the laser pistols from the cell. (00:50:40)
Plot hole: Because of the magnetic ore on the work clothes of the man who beamed up, the transporter made duplicates of everything put through it, and so couldn't be used. This was further complicated by the control and power circuits being blasted by the "evil" Kirk. However, the ship carries a number of shuttle craft, which no-one mentions.
