Deliberate mistake: After one of the enemy villagers stabs Nona, during the ensuing fight when Kirk does a flying dropkick on a villager, this semi-closeup and the next wide shot are both flipped shots - the leather band is on Kirk's left upper arm, instead of his right. (00:46:15)
Star Trek (1966)
1 deliberate mistake in A Private Little War - 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: Gene Roddenberry created the transporter as an easier (and cheaper) way of getting Enterprise crew members onto a planet's surface, rather than landing the ship on the planet.
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.