“Beam me up, Scotty” is never said verbatim in the original series.
Star Trek the original series is responsible for many iconic inventions, among them the Vulcan neck pinch and the Vulcan salute. Both were created by the actor playing Spock himself, Leonard Nimoy. The original Vulcan salute was intended as a slightly awkward half kneeling shoulder rub. Nimoy found that too touchy feely for the Vulcans and created the iconic hand gesture instead. Same goes for the famous Vulcan self-defense technique. The original script called for a punch to the head, which Nimoy found to undignified for his character.
Gene Roddenberry intended the original Star Trek to have a progressive political agenda, even though he had to sneak some scenes in and cut other ideas entirely. Roddenberry wanted Captain Pike’s number one to be portrayed by a woman, but the studio rejected the idea, as such a strong female character was seen as unrelatable. ‘Star Trek - The Next Generation’ took up the idea of a fully emancipated society and occasionally featured male extras in skirts.