What are some canon myths that keep perpetuating in the collective headcanon of fans?

That the Prime Directive only applies to pre-warp civilizations.
- Besides the fact that the Prime Directive is violated constantly, what am I missing about it?
  
  It's about interference with non-Federation governments and cultures in general. The Prime Directive forbids mucking about with Romulan politics, for instance. Worf gets away with a lot of things that would violate the Prime Directive in regards to the Klingon Government because he has dual citizenship and is a member of Klingon nobility.
  The ban on contact with pre-warp civilizations is also more specifically uncontacted pre-warp civilizations (you can chat with them if they're already buying Romulan ale from the Ferengi because the damage has already been done) and more generally pre-interstellar civilizations (warp drive is the usual way a civilization becomes interstellar, but there are alternative methods).
- You're not wrong, but man the Prime Directive would make a whole lot more sense if it did. The commonly misunderstood version of the PD that is intended to prevent cultural contamination is clear and simple. Given its status as the literal top rule, the actual PD—a generalized non-interventionism/pro-isolationism dictum—is oddly complex, vague, and lacking a focused objective.
  
  I still want the story of the one mousey, overworked lieutenant junior grade whose job it is to follow-up on all prime directive violations.
  Investigator: Alright, Captain, let's begin, shall we? Apparently you and your crew intervened in a labour dispute between two independent worlds, and taught the previously exploited civilization about unions, and now their entire social development has radically shifted. Is there anything in that basic statement you'd like to dispute?
  Captain: Uh...when did this happen?
  Investigator: Stardate 43012.7.
  Captain: That was eight months ago!
  Investigator: Correct. I've had an entire backlog to work my way through, and this is the earliest I was able to address your situation.
  Captain: Five months ago my entire ship was trapped in a time vortex and we all deaged to adolescence.
  Investigator: ...I did think you looked rather young.
  Captain: We don't even have any memory of those events, but it does sound pretty dope. Surely you can't hold us responsible for actions we haven't yet committed, and might not actually commit if we were put into similar circumstances again.
  
  All of this could be avoided if they'd just rename it to the Mind Your Own Business Directive.

The first television interracial kiss.
It wasn't even the first one on Star Trek.
- Yeah, I used to get tired of correcting that on Reddit. Given that it's almost a decade after British TV are recorded to have a had a black/white kiss, if anything is should be a source of shame that US TV waited so long, not pride.
  
  It’s going to be a long road for Paramount, and the Star Trek franchise, to get past it American-centric blinkers.
  IDIC seems to be an in-America rather than a global or universal concept for the executives and even most of the EPs.
  Defining ‘television history’ as just what was broadcast in the United States is all of a piece of Hollywood’s century-long understanding that it was the global entertainment focal point.
  Paramount is strategically moving to emphasize development and production outside the United States, and recently cut its domestic staff significantly. However, Paramount’s own communications team seems to remain quite blindly American-centric as if Paramount+ can survive on the US market alone. Geoblocked embedded video, predominantly American feature article writers and editors on the StarTrek.com official site, are all evidence of the persistent blind spot.
  But it’s hurt the franchise. There’s a kind of Federation Exceptionalism baked in that comes across as an expansion of American exceptionalism. When all the hero captains other than Picard, and many of the bridge crew, are identified as coming from what is currently the United States, it says that the US is still the most important place and marginalizes other countries.
  Star Trek’s impact outside North America has been constrained by these attitudes going back to the 1960s.
  Canadians, used to crossborder transmissions of US networks tend to roll with it, to the point that Star Trek shows are often the most popular dramas, and not just in the sci-fi genre. The UK and Germany got TNG in syndication, which built their base, but in much of the world Star Trek only became broadly accessible through Netflix.
  And what we hear in social media platforms like this one is that fans outside the US, who are attracted to and embrace Trek’s aspirational values, find these kinds of persistent markers of inward-looking American attitudes an irritant, at some points like nails on chalkboard, standing out against what Trek aspires to be.

Spock is the first or only Vulcan in Starfleet. The crew of the Intrepid would like a word.
These can be tough, since three generations of fans have worked on later shows or ancillary official materials. E.g. Startrek.com used to say that about Spock.
Lots about Klingon history: they stole warp tech from the hurq, the hurq (who came after Kahless and stole his relics) are the gods of ancient Klingon myth. Klingon warrior culture is a recent aberration (claims one lawyer whose parents were undervalued academics). Kahless lived a thousand years before TNG. That's only half the time since Surak or Charlemagne, but fans want to see him more like King Arthur or Robin Hood.
- T’Pol would be the first Vulcan in Starfleet, no?
  She started off as Vulcan High Command but officially joins Starfleet later on in ENT.
  
  And when Enterprise did that, there were fans who insisted it was a retcon. It's something people beleived since TOS even though it was contradicted pretty soon after the Federation was even established.
  There are several other things that fans have been certain of since the 60s (like saucer separation being irreversible in the field or Vulcans only having sex during Pon Farr) that weren't the production intention, but this one was blatantly impossible and it's very strange.
  
  She joined the United Earth Starfleet, though. If someone wanted to get really pedantic, they could claim there's a possibility she resigned her commission before the transition to the Federation Starfleet.
  But yeah, T'Pol, the senior staff of the USS Intrepid, the various admirals we've seen in Disco and SNW, all would have joined Starfleet before Spock.
- E.g. Startrek.com used to say that about Spock.
  Unfortunately, it still does.

That Vulcans cannot feel emotions because of their biology. They actually suppress them and have been trained to do that since they are children.
- "That Vulcans cannot feel emotions because of their biology."
  I remember that idea being prevalent years ago. I did not know that it's still making rounds.

That Klingons are honorable.
- Very true. We are misled by how Worf tries to be a stereotypically honorable Klingon because he is culturally human. He has little knowledge of how Klingons raised in Qonos understand honor.
  
  @concretebaby @rdh worf is like an adult religious convert who understands certain rules to be inflexible that people who grew up in the religion understand to be optional at best
- Also what humans perceive as honorable may not be the same what klingons see as honorable

My pet peeve, that warp drive works like the Alcubierre Drive. It doesn't.

Oh, here's a biggie. That individual ships in TOS had their own unique insignia. That turned out to be a myth, despite being perpetuated on-screen by ENT: "In a Mirror, Darkly".
It also led to a post of mine that was particularly controversial at the time.
- @khaosworks @concretebaby Oh wow. I remember reading this “fact” in Mr Scott’s Guide to the Enteprise or a similar technical manual in the 80s!
  
  You remember correctly. From Mr Scott's Guide to the Enterprise, p24:
  The great success of Enterprise's historic five-vear mission brought other changes to Star Fleet procedure. To honor the ship and her crew, Star Fleet Command unanimously elected in 2212 to drop the individual ship emblem system employed since 2206 and then adopt the insignia of Enterprise [Command Division] as the official insignia of Star Fleet. Each individual's branch department would no longer be denoted by shirt color; rather, this would be expressed by a colored, circular background on the uniform insignia. The basic uniform became a long- sleeved tunic of gray or tan, with foot coverings built into the uniform pants.
  (As you can see, the chronology here is way off, written as it was prior to TNG and the establishment of TNG's Season 1 in 2264 as per TNG: "The Neutral Zone". Mr Scott's Guide was based on the FASA Star Trek RPG timeline, which was in turn derived from the Star Trek Spaceflight Chronology.)
  To be fair, the whole thing stemmed from a production mistake in TOS: "The Omega Glory". The article I linked to is pretty interesting and explains how this happened. It was only until the memo surfaced that we discovered exactly what the original intent was.