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)
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: 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)
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.