Continuity mistake: Kirk and McCoy are in the Exeter's engineering section when Kirk uses the intercom to ask if anyone is aboard. Several shots of the deserted ship follow as his voice echoes off the walls, including one of engineering - with Kirk and McCoy suddenly, mysteriously absent. (00:03:45)
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.
Continuity mistake: After Spock's Brain is taken McCoy says he has no idea how long the body can last on life support without the brain. Somehow in the following few moments McCoy has established that Mr Spock's Body will die in exactly 24 earth hours. No explanation is given as to how he came up with this figure.
Continuity mistake: When Kirk exits the turbolift he sits in the captain's chair, and Yeoman Smith stands behind him with barely any space between them, but in the shot facing the main viewscreen Smith is gone, and in the next shot she reappears right behind Kirk again. Smith continues to disappear and reappear in following shots. (00:04:00)
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. (00:44:42)