Continuity mistake: Korob uses his wand to put a feast on the table and light the candles. Only, in the very next, close-up shot of him, the feast is gone and the candles are unlit again. Next wide shot, everything is back. (00:20:00)
Continuity mistake: In the dining hall, Korab leans over to listen to his cat. As he does, his right hand is at seat level. A second later, his right hand is up by his shoulder. (00:22:20)
Continuity mistake: When Sylvia angrily upbraids Korob for talking too much, an inserted reaction close-up of him makes the table and chairs change from in front of him to behind him and back between shots. (00:27:15)
Continuity mistake: When the giant cat breaks down the cell door, Korob falls beneath it face down with his head toward the door. In the very next shot, he's in a completely different position - face up with his feet toward the door. (00:43:30)
Revealing mistake: Near the end of the episode, after Kirk has destroyed the orb, we see Korob and Sylvia in their true form. As they move, you can see the black strings used to manipulate the puppets.
Continuity mistake: After the heavy door lands on Korob, his right arm is straight down by his side. The next shot of Korob shows his right arm extended away from his body.
Factual error: Kirk, McCoy, and Spock are chained to the dungeon wall, with McCoy noticing he is next to a skeleton, also chained. This is incorrect, as a skeleton's bones are held together by cartilage, which would rot over time. Therefore, the skeleton would not be hanging intact, but would be a pile of bones on the floor.
Suggested correction: As we learn in the episode, the 2 aliens created the entire castle only recently to appeal to the human's primal fears and superstitions. A pile of bones on the floor would not have the frightening impact of a hanging skeleton.