Continuity mistake: Vera fires the gun several times, and later tells Justice Wargrave that the gun is empty, meaning that all the cartridges in it would be spent. When the judge loads his one bullet into the chamber, he does so in a gun where all five cartridge svisible are unspent.
Character mistake: Rob is having a nightmare, part of which involves the disappearance of his thumbs. When he finds Laura at home, the script calls for him to say, "I want you to help me get my thumbs back," but he actually says, "I want you to help me get my thumb backs." His thumbs are also still there but hidden (you can see a portion of them in one frame of the episode).
Other mistake: In the final scene, Kirk is still in the transporter room, but does not have on a visor when the ambassador transports out. Even if he did, humans can still go mad if wearing one and that's why Spock operates the transporter. Spock has his visor on, but then you see Kirk walk out of the transporter room without a visor and he is not going mad.
Continuity mistake: After Lucy tells Mr. Merriweather that he's invited to the seance, when it cuts to Lucy unfolding the card table legs, note the couch behind her with one normal seat cushion on the left, but in the next wideshot there's an additional shorter cushion under the normal cushion. The small towel also repositions itself neatly on the couch. (00:11:55)