The cast wore oversized versions of their costumes as their characters aged in order to give the impression that they were shrinking.
Having been born on July 16, 1882, Felix Locher (Robert Johnson) was the earliest born actor to appear in any "Star Trek" episode or film.
William Shatner resisted looking too old as Captain Kirk aged. This is why at first the aging Kirk's hairline is receding but later his hair is more full.
Kirk's age (34) is established in this episode. William Shatner was 36.
Kirk reuses the scam involving the "corbomite" device, which he first described in The Corbomite Maneuver (1966). Although Chekov was not on the bridge on that occasion, he obviously heard the story from someone, as he and Sulu exchange knowing looks when Kirk mentions the word.