Contrary to popular belief, Captain Kirk never said "Beam me up, Scotty" in any episode or movie.
Stardates were established in order to keep the audience guessing as to when the series takes place. A calendar year for the adventures of the Enterprise crew is never given in any episode, and Gene RoddenberryGene Roddenberry said the series could have taken place anywhere from the 21st to the 31st Centuries. By the time of [Star Trek: The Next Generation], however, calendar years for Trek adventures had been established and the official [Star Trek] chronology now indicates that the original [Star Trek] TV series takes place between the years 2266 and 2269.
On at least two occasions ({Miri} & {City on the Edge of Forever}) the exterior Mayberry set from "The Andy Griffith Show" was used. In {City}, as Kirk walks Edith home, they pass by the easily recognizable courthouse, Floyd's barbershop, Emmett's repair shop, and the grocery.
In the hallways of the Enterprise there are tubes marked "GNDN", these initials stand for "goes nowhere does nothing".
The transporter was a plot device intended to eliminate the pacing and production problems involved in depicting the ship landing and taking off all the time. Budgetary constraints on effects were also a consideration. The first landing of a starship would not occur until [Star Trek: Voyager] episode #2.1, [{The 37's}], broadcast 28 August 1995.
Gene RoddenberryGene Roddenberry originally conceived the Klingons as looking more alien than they do in the series, but budget restriction prevented this. When Star Trek moved to the big screen, he was finally able to make Klingons look more alien. The resulting continuity break between TOS and the movies and later series was finally addressed in the [Star Trek: Deep Space Nine] episode {Trials and Tribble-ations} in which the character of Worf confirms that something did happen to make the Klingons appear human, but he refuses to elaborate.
Early drafts for the Harlan EllisonHarlan Ellison episode {City on the Edge of Forever} included a guest character, an Enterprise crew member who dealt in addictive drugs; it was this character who escaped into the past, via the Guardian of Forever. Gene RoddenberryGene Roddenberry asked him to change this element, on the grounds that no member of *his* crew would ever use or deal in illegal drugs. According to Ellison's account in the book 2895's the City on the Edge of Forever: The Original Teleplay That Became the Classic Star Trek Episode, for years after the series was cancelled, Roddenberry said that Ellison's original draft had been unusable because "he had Scotty dealing in interplanetary drugs" - although Mr. Scott does not even appear in that draft.
[?] Victor Lundin appeared in the show Errand of Mercy. Although he did not have a speaking part he was the first Klingon to appear in the original [Star Trek] series.
McCoy, in a drug-induced madness, travels back in time and changes history. It is now up to Kirk and Spock to follow him back and set everything right.
