Character mistake: Spock says "The Queen of Hearts and her cards are characters from Alice Through the Looking Glass, Captain." They are from Alice in Wonderland. Looking Glass has chess pieces as characters instead of playing cards.
Beyond the Farthest Star - S1-E1
Continuity mistake: There is an alien in a Starfleet gold shirt sitting next to Sulu. For a second, there is a human in a Starfleet red shirt, then it goes back to the gold shirt alien. (00:01:50)
Trivia: The animated series featured the first appearance of the Holodeck (called the Rec Room) in this episode only. Gene Roddenberry wanted to use the Rec Room/Holodeck idea in the original live action series of the 1960s, but found that budgetary constraints were prohibitive at that time. The Rec Room finally appeared once in the animated series, in this episode, in 1973. It wouldn't be seen again until Star Trek: The Next Generation, in 1987, some 14 years later.