Plot hole: Apparently there is some confusion over the distance between Earth, Starbase 11, and Talos IV. When Spock first meets Pike on Starbase 11 he tells Pike Talos IV is only six days away. Yet when Pike (in the recording) speaks to the Talosians for the first time, he says he is from a star system on the other side of the galaxy. If Talos IV was on one side of the galaxy and Earth was on the other side, it would take hundreds of years at maximum warp to travel from one planet to the other.
Character mistake: Spock expresses amazement that the natives of this planet speak Earth English, however, he and Kirk were both on the bridge when Uhura tapped into the planet's news broadcast and already know that they speak Earth English, and there's no reason to tell McCoy, because he heard it too. Commenting on it would be illogical.
Character mistake: Spock tells Kirk that without being able to test their vaccine with the ship's computers, "it could be a beaker of death." The vessel that the vaccine is contained in is a flask, not a beaker. The ship's science officer should know the difference.
Other mistake: On some VHS editions of this episode, the back cover features a picture of what appears to be both good and evil Kirk sitting at a table, however this never happens anywhere in the episode. That picture is actually from the episode "What Are Little Girls Made Of?"
Continuity mistake: When Scotty awakens in the sick room after being attacked by Nomad, Nurse Chapel has her hands placed on him. In the next shot, when McCoy tells Scotty to take it easy, Nurse Chapel's hands are no longer on Scotty, and in the next shot, her hands are back on him.
Continuity mistake: The Klingon is standing on a hillside above Maab, yet when he fires his phaser, the beam streaks upward. From that angle, he wouldn't have hit anything but sky. Nevertheless, the beam somehow re-angles itself downward so that it hits and kills Maab.
Continuity mistake: Mr Checkov has a rather unfortunate hair styling during the beginning of his role in Season 2. In this episode his hair is normal until the end, where in between being given an order and carrying it out he somehow manages to go and have his hair professionally done and made all bouffant.