As they beam down to the planet Sarpeidon some three and a half hours before their sun, Beta Niobe is about to go nova, Kirk, Spock and McCoy meet Mr. Atoz (Ian Wolfe), standing vigilant against the few remaining hours left for the planet. Upon reflection, it didn't have to be such a mystery what Atoz's mission was; he could have explained it all very logically to his visitors. Presumably the only apparent reason for the forced misunderstanding was to send the Enterprise crew off into different directions through the library's time portal, thereby justifying the story.
As we've seen in other Season III episodes, the series was taking advantage of Spock's workmanlike and serious Vulcan nature, and turning those conventions on their head to provide him with human emotion. In this one, with Spock and McCoy both trapped some five thousand years in the past, Spock begins to regress to the baser instincts of his Vulcan roots, feeling jealousy and rage as he begins to fall for cave-girl Zarabeth (Mariette Hartley). Eventually McCoy prevails with his own logic, but I have to wonder, would it have killed the writers to have Spock give Zarabeth a good-bye kiss when he left?
Best line of the show for me had to do with the Captain's saving a Salem witch from an angry mob. Once safe, she says to Kirk - "I thought I'd be limbered sure when that gull caught me cuttin' his purse". But the concept that really blew me away was that first look at a future technology when Atoz introduced the atavachron. Who would have been able to say back in 1969 that we'd be watching Star Trek episodes over and over again on little round discs?