Tomorrow is Yesterday - S1-E20
Factual error: Towards the end of the show the Enterprise is leaving Earth orbit and heading towards the sun. We see the Earth diminish and the moon appear looking exactly as it does from Earth. From this angle we should be seeing the "dark side" of the moon, which looks completely different. (00:40:50)
Factual error: In the opening scene on the bridge, when Spock states the planet's properties, the circumference is given in US miles; the mass is given in metric tons; the density is given in metric grams per cubic centimeter; and the atmosphere is given as oxygen/nitrogen. No scientist of Spock’s standing would mix US and metric unit systems. The atmosphere composition should also be stated reversed as “nitrogen/oxygen” with the most abundant gas first. (00:42:00 - 00:59:00)
The City on the Edge of Forever - S1-E29
Factual error: This episode takes place in NYC during the 1930's, but after McCoy's phaser is stolen in the exterior shot of the buildings a fallout shelter sign can be seen. These signs were put up no earlier than 1961.
The City on the Edge of Forever - S1-E29
Factual error: Edith Keeler says to McCoy, "My young man is taking me to see a Clark Gable movie." In 1930, Clark Gable was an uncredited bit player who had last made a film in 1926 - Edith, a New York charity worker, would not even have encountered his name.
Factual error: When they are searching for Finney hidden somewhere in the ship, all ship noises are deadened, and the heartbeats of those on the bridge are muffled by McCoy. In order to locate Finney's heartbeat the ship's auditory sensors are magnified by "one to the fourth power". That's 1x1x1x1 = 1, ie no magnification.
Factual error: Mr. Spock states that the asteroid is almost as large as the Earth's Moon. Such big bodies must be predominantly spherical due to their own gravity. However, the asteroid is very elongated, with a very irregularly shaped surface. (00:06:40)
Is There in Truth No Beauty? - S3-E5
Factual error: The Enterprise accidentally travels a short distance outside the galaxy and can't find its way back. But they'd have to travel for months to get so far outside the Milky Way that they couldn't, well, just turn around in the void and see it. Our galaxy is huge. 100,000 light years across. Very huge. And that barrier may surround the galaxy, but even it is big, pink and visible.
Factual error: When Kirk is given the medicine badge, it's a stretchy elastic/Spandex headband. This is supposedly a completely pre-industrial culture paralleling the early Native American tribes. They have no fabric, no yarn, no spinning wheels - only hides and animal hair, neither of which can stretch a la Spandex. (00:14:40)
A Taste of Armageddon - S1-E24
Factual error: How do the Eminiarians fire a weapon based on sound ("Decibels - 18 to the 12th power") up into the vacuum of space at the Enterprise?
Factual error: Spock says the Klingon ship is approaching at Warp Six, but Sulu counts off the distance at about 50,000 kilometers per second - that isn't even the speed of light.
Factual error: Trelane has been watching Earth as it was 900 years ago (14th century in the film), but his style is more 17th century, and he mentions Napoleon who lived in the 19th century.
Factual error: The harpsichord Trelane plays is far too short and has pedals like a piano.
Factual error: In several episodes, when the Enterprise has to turn "hard about", we see it banking to one side like a jet plane. The Enterprise has no wings, and they're in space. No banking.
Factual error: If Miri's planet is a "duplicate" (meaning identical) Earth, it should have clouds. It doesn't. This remains a mistake because "duplicate" means "exactly the same," and thus the clouds should be there. The special effects crew forgot to put them in. Noteworthy: the very first thing fixed in the digitally enhanced version of this episode was the duplicate Earth. It has clouds now. (00:01:30)
Factual error: When Kirk/Spock enter/leave the Council Chamber, the doors quietly open unaided (as though there were motion detectors in operation), yet the Organian culture - determined by Spock to be approximately Class D minus on Richter Scale of Cultures - would not have had such technology. A fact overlooked by Kirk and more importantly, Spock.
Shore Leave - S1-E16
Factual error: In a scene where Kirk and McCoy are examining the tracks left by the White Rabbit and Alice, in the background behind some trees can be seen a white building (the shoot was done at Africa, USA, an animal theme park). (00:13:30)
Factual error: As Kirk, McKoy and Scottie age during the episode, their hair goes from brown to fully grey. Mr. Spock shows this to a lesser extent, but by the end of the episode, he has full streaks of grey. This isn't how grey hair works. It starts from the root and works it way outward over time to the end of the strand. Unless their hair is growing quite rapidly, and then cut to keep it short, they shouldn't have full heads of grey hair.
The City on the Edge of Forever - S1-E29
Factual error: The song "Goodnight Sweetheart" was written and first performed in 1931. This episode takes place in 1930, one year before.
The City on the Edge of Forever - S1-E29
Factual error: Spock picks a lock during the great depression, but the lock is from the late 50's.
Factual error: Throughout the episode, there is a constant reference to 5 p.m. being the time Kirk and crew (a.k.a., the Clanton gang) were to die. However, the real 30-second shootout was at 3 p.m.
Suggested correction: That might only true in today's standards. But we have no idea what future generations will choose to make standard.
Bishop73
This is such a trivial criticism that it should be removed to be fair. Whatever measurement standard is used in the future, it will be uniform without mixing of different unit systems.
Ken S
But that's an assumption based on what you think the future would be like. The British and Americans currently use a mix of different unit systems. While many US students use miles and pounds, they still calculate density as g/cm3.
Bishop73
No scientific or engineering facility on Earth uses imperial measures nowadays, including NASA. That is not going to change.