Continuity mistake: The lawgivers' robes that Kirk and Spock take off and drop on the floor just inside the doorway disappear after they phaser the wall to reveal Landru. The robes reappear a few minutes later, but have now migrated several feet to one side, bunched up against the wall where they are no longer in tripping range of the actors about to enter the scene.
00:42:25 - 00:45:00Jean G
Other mistake: On the bridge, as the camera looks at the view screen, there is a flashing blue light reflecting on the console in front of Sulu, but there is no light other than scanner under the viewer flashing and it's too far away to project light that far, and it's amber colored.
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Continuity mistake: While Kirk is attempting to convince Marplon and Reger to take them to Landru, a distant shot shows Marplon's right hand descend from his chest to his side. Immediately thereafter, a close-up shows Marplon's hand again suddenly at his chest.