Robert Walker was 26 years old when he played 17-year-old Charlie Evans in "Charlie X".
Michael J. Pollard (27 years old) and Kim Darby (19) play pre-pubescent children in "Miri".
Fake Nationality: William Shatner and James Doohan (both Canadians) play an American and an Scotsman, respectively. Walter Koenig is a partial case: his parents were Russian Jews but Koenig himself was an American citizen playing the Russian Chekov. Nichelle Nichols (an American) played Uhura, whose native language is established as Swahili, implying Uhura is from somewhere in eastern Africa. Worst of all was Mexican Ricardo Montalban playing the implied South Asian Khan Noonien Singh.
George Lucas Altered Version: The 40th anniversary "Remastered" versions (also known as TOS-R), which (contentiously) replace the original practical effects (mostly involving ships, planets and their skies, and phasers) with CGI.
Hey, It's That Guy!: Lt. Cdr. Gary Mitchell in the second pilot "Where No Man Has Gone Before" is played by Gary Lockwood, who also played Dr. Frank Poole in 2001: A Space Odyssey. No wonder HAL wasn't too happy with him...
Life Imitates Art: This show inspired so many things - including possibly its ultimate triumph, as Nichelle Nichols's role on the show was the inspiration for Dr. Mae Jemison, America's first female African-American astronaut, who later did a cameo on Star Trek: The Next Generation.
And for the Bluetooth headset.
The show is often credited as the inspiration for cell phones, but it also accurately predicted the tablet PC.
The military and many high-level police agencies are experimenting with non-lethal heat and sound beams to disperse riots and disarm attackers without killing them. Phasers On Stun anyone?
No Budget: In order to cut costs, incidental music avoided scoring anything for violins. Melodies in the strings are played by violas. Violinists charge that much more, apparently.
The Other Darrin: Shatner's predecessor, Jeffery Hunter, played Captain Pike in "The Cage". This footage was later re-used in "The Menagerie", with Pike himself appearing a motionless deformity in an iron lung-type device. This was primarily to disguise the fact that Hunter was unavailable; this new Pike was played by a lookalike (such as he is) named Sean Kenney. What's interesting is that Captain Pike was retconned into Kirk's predecessor, as well; He was the original Captain of the Enterprise, with Mr. Spock as his science officer. This is still canon in the Abrams film, in which Bruce Greenwood plays Pike.
Kenney would later appear as a bridge crewmember in "Arena" and "A Taste of Armageddon".
Red Shirt: Although the Trope Namer, the first red-shirted casualty doesn't appear in series until episode 7 ("What Are Little Girls Made Of?"); the very first casualties are blue-shirted Science Team and gold-shirted Command squaddies.
The Rural Purge: Inverted - it should be noted that the demographic information that led to the Rural Purge wasn't available from Neilsen before 1970 or so; had it been, Trek would've benefited since it attracted advertisers' favored demographics.
Serendipity Writes the Plot: The transporter was created because it would be too expensive to have the crew land on the planets in a shuttle every episode.
Throw It In: According to legend, the stagehands didn't like Shatner very much, so in the episode "The Trouble With Tribbles," they continued the avalanche of tribbles much longer than was scripted (including the final tribble that bounces off his head at the end). Shatner can clearly be seen glancing up at the prop men with annoyance.
During production of "Where No One Has Gone Before," Gary Lockwood found the silver contact lenses painful and difficult to see through. Gary Mitchell's imperious stare is a result of Lockwood having to look down his nose through the pinholes in the lenses.
The Vulcan mind-meld, neck pinch and salute are all examples of this. All were suggestions made by Leonard Nimoy. In the case of the first two, they replaced more mundane, conventional ideas in the original scripts (respectively, a simple interrogation in "Dagger of the Mind", and Spock slugging evil Kirk with a pistol butt in "The Enemy Within").
Vindicated by Reruns: Possibly the Trope Codifier. It was a modest ratings success until NBC developed the habit of switching its timeslot around. The extensive rewriting of scripts and lack of immediate success made many of its more talented writers leave, which caused the quality to slip noticeably in a short time. It was canceled after the second season, but quickly Un-Canceled following an extensive letter-writing campaign from its fans. The third season saw even worse ratings, and NBC canceled it for real. Shortly afterwards, American television industry discovered the use of demographics. When stations noticed that, according to the new standards of how ratings were calculated, Star Trek should have been one of the most successful shows on TV (and that NBC had killed what could have been their golden goose), they were rushing to throw on Star Trek reruns to attract the young demographic that it had been popular with. It didn't take many years of reruns before the show's modest fanbase grew into a force to be reckoned with. The rest is history.
Actually, the producers had Nichols read Spock's part in her audition because the Uhura part hadn't been written yet or even named. She had them describe Spock's character to her, instead of Uhura, "so you can see whether or not I can act."
The episode "Spectre of the Gun" (the one set at the O.K. Corral) was originally planned to be filmed on an existing Western town set on the backlot. However, serious budget cuts for the series' third season made this impossible. So, it was instead made on a soundstage in a surreal, incomplete, plainly artificial environment. Though some (including Leonard Nimoy) were skeptical over this move, it's now largely viewed to have been a good choice for the story.
James Hong (a.k.a. David Lo Pan) auditioned for Sulu, but was passed over in favor of George Takei.