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.
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.
Continuity mistake: After Korob fails to get information, he tells Scott and Sulu to take them out. They escort Spock and Kirk over to the door past McCoy, but don't stop (apparently DeForrest missed his cue.)
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.
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.