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)
Continuity mistake: When Kirk and his landing party beam down to the planet there are six shots of Morg, who have their right arms covered in fur in all those flipped shots, but when Morg attack the landing party it's their left arms covered in fur. Presumably, the first six shots were flipped for direction continuity. (00:13:15)
Revealing mistake: It would seem that with the incredible advanced knowledge and furnishings that have been bestowed upon the Imorg down below, the 'Teacher' should have at least provided them with adequate high tech structuring and not the ratty, torn and warped substandard sheet rock seen on the bottom of the walls in these two camera shots. Yep, they can remove and restore a brain but can't find a place to buy good quality plasterboard. (00:23:40 - 00:33:51)
Continuity mistake: When Scotty, Kirk, and the others follow Spock's signal to the chamber with the Controller, they encounter Kara and she activates their pain bands. Spock's body has a pain band around his waist as the other men drop to the ground, but after McCoy tells Kirk, "Spock, no pain," the pain band is missing from Spock's body, then in the next shot it reappears when he goes after Kara's bracelet. (00:35:05)
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.
Factual error: In the opening sequence, Spock identifies the alien ship as possessing "ion propulsion" which he says is "unique technology." Scotty is similarly impressed and says, "They could teach us a thing or two!" Kirk later comments that "Advanced ion propulsion is beyond even our capabilities." However, even back in the 1960s, ion propulsion was physically feasible, while Warp propulsion was complete fantasy. Ion propulsion of any kind could never even reach lightspeed and would be incredibly primitive compared to Warp technology. In fact, we in the 21st Century have already developed ion propulsion, but it will probably take many hundreds or thousands of years to develop anything even close to Warp technology.
Audio problem: During the scene where Kirk is talking in the briefing room, the director was obviously not pleased with how James Doohan said his lines. Due to budget constraints, instead of re shooting the scene, they simply replaced Mr Scotts dialogue with another one. You can see it since at one point his lips are completely out of sync, even on the remastered edition. (00:06:40)
Other mistake: When Chapel comes into Sickbay and looks at the "dead" Captain, the camera goes to close up of Kirk, and he wakes up. After she yells for McCoy, the camera goes back to Kirk, and he goes back to sleep. The motions of him waking are obviously played in a slow reverse instead of him quickly closing his eyes.
Plot hole: In the conference room, Spock informs Kirk that his theory of a Romulan cloaking device kept the sensors from detecting the ships. However, in S1:E14, "Balance of Terror", they figured out the cloaking device, and how it worked. Unless he was feeding into the deception, Spock shouldn't have had any theory when it was a fact.
Factual error: When Kirk is given the medicine badge, it's a stretchy elastic/Spandex headband. This is supposedly a completely pre-industrial culture paralleling the early Native American tribes. They have no fabric, no yarn, no spinning wheels - only hides and animal hair, neither of which can stretch a la Spandex. (00:14:40)