The episode "Plato's Stepchildren" sees the crew at the mercy of telekinetic aliens who have modeled their small civilization on the teachings of the title philosopher. This episode has a historic moment between William Shatner and Nichelle Nichols, one that was guaranteed to happen when Shatner intentionally blew coverage takes that omitted this historic moment. What happened in this episode that was a first for U.S. network television (we'll be liberal on the wording).
First interracial kiss