Deliberate mistake: When the Klingons post signs for their rules, they're printed in English. The Klingons have their own language, and people on Organia most certainly aren't English speakers. Even if the Universal Translator allows Kirk and Spock to hear in English, it wouldn't change the look of a sign.
Star Trek (1966)
1 deliberate mistake in Errand of Mercy - chronological order
Is There in Truth No Beauty? - S3-E5
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.
Trivia: The Vulcan Nerve Pinch was invented by Leonard Nimoy as a way for Spock to overpower opponents without having to resort to violence.
Question: When Kirk and crew neutralized all the androids on the planet, what happened to the androids on the Enterprise running the ship?
Answer: If all the humans beamed down and only Androids were on the ship as Larry Mudd said then how did they get back aboard the Enterprise if all the robots were shut down.
Answer: After causing Norman to overload, all of the other androids shut down. The same could be said for the androids on the Enterprise.