Other mistake: Kirk's voice-over log entry says he's been "placed on the surface of an asteroid." The Metrons earlier referred to it as a planet prepared for them with a suitable atmosphere. How and why does Kirk suddenly assume that it's an asteroid rather than a full sized planet? As an experienced space veteran, Kirk, who has already been told that it's a planet, would never make such a mistake. (00:23:45)
Other mistake: Scotty has a science patch on instead of the engineering patch in this episode.
Revealing mistake: A re-used sickbay scene taken from an earlier episode causes Nurse Chapel to instantly revert to her old hairdo as the sound waves make her fall unconscious. (00:41:00)
Visible crew/equipment: A camera shadow briefly intrudes on the right side of the screen as Kirk asks Mr. Scott about the sensor readings. (00:00:55)
Audio problem: When Kirk demands to know who the Troglytes are, his voice is dubbed over: his lips don't move at all. (00:04:05)
Continuity mistake: During Spock's Court Martial, Chekov says that General Order 4 is the only exception to Starfleet's no-death-penalty policy, and Sulu and the others agree. However, according to "The Menagerie," that exception is General Order 7, not 4.
Shore Leave - S1-E16
Character mistake: When Spock beams down after calculating there was just enough energy left for him to do so, Sulu and Kirk watch him materialize, and Sulu says, "Someone beaming down from the bridge." From the bridge? Shouldn't he have said "from the ship"? No one ever beamed down directly from the bridge, but even if they could, how would Sulu know that's where they'd come from? (00:28:00)
Continuity mistake: Korob uses his wand to put a feast on the table and light the candles. Only, in the very next, close-up shot of him, the feast is gone and the candles are unlit again. Next wide shot, everything is back. (00:20:00)
For the World is Hollow and I Have Touched the Sky - S3-E8
Continuity mistake: After he falls unconscious onto the blue rug, McCoy's position relative to the rug's top edge keeps changing between shots. (00:36:40)
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.
Shore Leave - S1-E16
Revealing mistake: There is a wooden or straw hut - some kind of man-made structure - visible in the lower-left of the frame behind Kirk and Bones as they walk. (00:12:30)
Where No Man Has Gone Before - S1-E4
Revealing mistake: After the ship enters the galactic barrier, when Kirk orders "navigation on automatic" there are flashes of light, and in a closeup of the first console just to the left of the main viewscreen, we can see the special effects material spread across the panel below the controls, for the fire to burn when it explodes. Then it cuts to the wideshot as a second console (near Spock's station) blows up, but in the background that first console is intact - no fire/damage whatsoever (it explodes again in a following wideshot). (00:10:00)
Continuity mistake: Isis is an all-black cat, but in a few shots, her "stunt double" with white paws can be spotted. The cat lying on the floor of the transporter room when Gary Seven beams aboard is a white-pawed double.
Continuity mistake: When Kara renders the landing party unconscious, Kirk falls with his arms splayed out to each side. But in close-ups, he has one hand folded over his chest. (00:23:30)
Continuity mistake: When Kirk sits down to consult the computer, the big green potted plant on the shelf behind him is there in full shots and missing in close-ups. It's much too large to be completely hidden behind him: if it shows up behind his head in full shot, it should show in close-ups, too, but it doesn't. It's not there. (00:16:30)
The Corbomite Maneuver - S1-E11
Continuity mistake: Spock states that the Fesarius (Balok's ship) "must be a mile in diameter". Yet any one of the small spheres that make up the Fesarius dwarfs the Enterprise. If the Enterprise is about 300m long, the Fesarius would have to be around 6 km in diameter - considerably larger than a mile.
Is There in Truth No Beauty? - S3-E5
Continuity mistake: Kirk aims his phaser at a berserk Spock's head and fires, but the beam hits him in the stomach.
Continuity mistake: At the end, the flag is brought in, and Kirk stands up - but in the next close-up of him, he's sitting down again. Next full shot, he's standing once more. (00:36:25)
Shore Leave - S1-E16
Revealing mistake: Stock footage turns the single plane strafing Rodriguez and Angela into two attacking planes for a moment. It becomes one plane again when it flies over Kirk and company. (00:33:40)
Suggested correction: They're on a planet where their every thought can be almost instantly created in physical form. Within the context of the episode it wouldn't be unusual to see literally anything in the background. Perhaps one of them was thinking about something involving that structure and it was being constructed for them.