Other mistake: In the final scene, Kirk is still in the transporter room, but does not have on a visor when the ambassador transports out. Even if he did, humans can still go mad if wearing one and that's why Spock operates the transporter. Spock has his visor on, but then you see Kirk walk out of the transporter room without a visor and he is not going mad.
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.
Revealing mistake: "Trek's" new 3rd season uniforms were tighter-fitting than their velour predecessors, presenting a problem for some actors. When the landing party beams down in this episode, the outline of William Shatner's tummy-wrapping girdle is very visibly showing through his costume. (00:13:10)
Revealing mistake: During the Court Martial scene, a directorial error led to Kirk's exit from the briefing room in the wrong direction. He walks off screen into what would have been a solid wall or corner. The briefing room's only door is on the other side of the room. (00:39:15)
Continuity mistake: After Garth attempts to convince Mr Scott that he is Captain Kirk and to beam him up, while he is banging his fists on the floor in anger he transforms back into himself and the fly like ring on his finger breaks and slides out of shot. It's quite hard to see but it does. The next time we see Garth's hand his ring is intact yet he has not transformed himself again to repair it.