Plot hole: When the Medusan Ambassador Kollos and Dr. Jones materialize, the latter is wearing a protective visor and Mr. Spock can see that. Spock then mistakenly addresses Dr. Jones as Ambassador Kollos. Spock's suddenly illogical mistake seems odd: why should the Ambassador need to wear a visor? Shortly after, why do both Jones and Spock wear visors while carrying the Ambassador's still closed gasket to his cabin?
Continuity mistake: As Kirk talks to Chekov on the screen, his hands are flat on the table, and there is a collection of data tapes in front of him. After the angle change, his hands are clasped on the table, the tapes have been replaced by a data pad, and Kirk appears to be frozen.
Continuity mistake: After Spock tells Boma and Gaetano that he's in command and they should fire only to frighten, not to kill, one of the creatures throws a spear and then his shield at the trio, and when the shield hits the ground it's much smaller than the huge shield lying on the ground in the next close-up.
Visible crew/equipment: When Lenore arrives at the Leighton's cocktail party, there is no furniture behind Kirk in the center of the room where they will stand in a moment. When Kirk introduces himself, in the next three shots facing Lenore, in front of her arm we can see a bit of camera equipment at the bottom of the screen.
Continuity mistake: After Kirk introduces himself to Lenore at Leighton's cocktail party, when she tells him, "Karidian is a most unusual man... That was my father," Lenore holds the goblet in her left hand as she takes a sip, but next shot the goblet is suddenly in her right hand as she sips.