While at the launch base and showing his ID to the security person, Mr. Seven shows a National Security Agency credential card. The NSA was one of the worst kept government secrets, but was not publicly acknowledged until nearly 25 years after this episode originally aired.
Spock mentions all the events which are to occur on that date the Enterprise travelled back in time to the 20th century and met Gary Seven. Among the events mentioned was an important political assassination. As it turned out, there were ultimately two important political assassinations in 1968: just six days after this episode aired on March 29, 1968, Reverend Martin Luther King Jr. was shot and killed in Memphis, Tennessee on April 4, 1968, and two months later, on June 6, 1968, Senator Robert F. Kennedy was killed in Los Angeles, California on the night that he won the California Democratic presidential primary.
This is the only episode of Star Trek in which time travel is treated as "routine." The Temporal Prime Directive does not yet appear to have been proposed, least of all taken effect.
This is the only episode of Star Trek in which a guest star is listed after the opening credits rather than in the end credits: "Guest Star Robert Lansing as Mister Seven" is displayed when the character is first shown in the transporter chamber.
The script called for Isis the cat to make various cat sounds on cue (meows, purrs, growls, etc.) Since finding appropriate real cat sounds for the soundtrack proved problematic, the director discovered that Barbara Babcock, who was hired to do the voice of the Beta 5 computer, could vocalize convincing cat sounds.
Bruce Mars: Finnegan from Shore Leave (1966) can be briefly seen as a New York Police Department officer.