Visible crew/equipment: After Kirk's briefing regarding Mitchell's abilities, when Spock and Kirk are alone just as Spock says that they'll never reach an earth base with Mitchell aboard, the boom mic casts a shadow overhead until Spock steps forward, and a bit can be seen again when Spock tells Kirk that it's his only choice.
Continuity mistake: When the Thasians restore Yeoman Rand.on the bridge she's barefoot, but when Charlie begs Kirk not to let the Thasians take him because he can't live with them anymore, we see Rand wearing a white fluffy slipper (which she wasn't holding when she reappeared), then she's back to being barefoot again.
Visible crew/equipment: After Uhura tells Kirk that "Captain Ramart of the Antares is on D channel," Kirk and Charlie head to the bridge, and when it cuts to Uhura the actor's tape mark can be seen on the floor behind her, where Charlie will stand when he steps out of the turbolift.
Visible crew/equipment: After McCoy examines Charlie and they talk about how Charlie learned to talk by just listening to the ship's tapes, when Charlie stands up the two actors' marks can be seen on the floor - the short one for Charlie and the longer one for McCoy, where they both will stand momentarily.
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.
Continuity mistake: When Uhura tells Kirk that she's made contact with his private transmitter she's seated at the communications console, but after the contact's been broken when she tells Kirk, "It's impossible at the moment because they stopped broadcasting," in this shot facing Uhura the turbo lift is not behind her - she's at a different station on the bridge - then she's back to where she was once again.
Visible crew/equipment: After the Klingon vessel's attack on the Enterprise, while returning fire just as Kirk orders to maintain firing range at 100% dispersal pattern, the set's unfinished wood plank with grey paint drip marks can be seen at the bottom of the screen. Additionally, at the end when Spock goes to stand beside Kirk's chair (also when he walks away) the actor's mark can be seen on the floor by Spock's feet.
Continuity mistake: In the first scene when Spock is piloting the shuttle craft out of the Enterprise and into space, as the bay doors open you can see both the ship's shuttles, the Galileo, and right behind it the Columbus. Yet as soon as the Galileo clears the bay doors, in the immediate reverse shot, the bay is empty and the Columbus has disappeared.