These are what we call the 'YMMV items.' Things that some people find in this work. We call them 'your mileage might vary' because not everyone sees these things in the same way. This starts discussions in the trope lists, a thing we don't want. Please use the discussion page if you'd like to discuss any of these items.
Dan: So Star Trek and Next Gen are about a resource rich society that is in such a creative rut they will send the Enterprise, humanity's finest ship out to unexplored corners of space just to find new life and new civilisations. Novelty is the most precious commodity there is! This is a profoundly bored people, so jaded, that they will load up their children and women onto a heavily armed warship and send it just out... just go! Just go somewhere and find me something interesting and tell me about it?!
Contested Sequel: Star Trek XI (referred to by some fans simply as 'the Abrams film' or similar) has caused a Broken Base within Star Trek fans between people who only like the old Trek, people who only like XI, and people who like both.
Creator Worship: The Great Bird of the Galaxy himself. Rick Berman, Ronald Moore and J. J. Abrams are a bit lower on the hierarchy. Brannon Braga is, unfortunately, often villainized for what happened with Voyager and Enterprise.
Fan Dumb: Quite possibly Ye Originale Fan Dumb, at least in the sense we think of it today. Mercilessly skewered in the documentary Trekkies, which featured the juror who wore her Star Fleet uniform to court and one fan who seriously thought about getting his ears surgically altered to look Vulcan.)
Ho Yay: Every series has at least one hugely popular slash pairing, and sometimes more than one. Slash fans will insist these characters want nothing more than to do each other, no matter how heavily contradicted by canon.
Kirk/Spock (or Spirk) is the original Slash pairing.
Archer/Reed, Tucker/Reed and Reed/Hayes from Enterprise.
Hilarious in Hindsight:: In the 30th anniversary special, there is a skit featuring the cast of Frasier sserving on the USS Voyager under Janeway. At one point, a Klingon beams aboard with the dog, which had been digging up azalea bushes on the Klingon homeworld. Janeway remarks, "Now you see why we shouldn't have pets on starships".
Mary Suetopia: Roddenberry's vision for Trek, but especially the first season of Star Trek: The Next Generation.
The Problem with Licensed Games: Star Trek has been notoriously variable with the quality of its forays into interactive entertainment - partially because distilling the essence of the best episodes of the series into a truly interactive format is goddamn hard. The "best" Trek games to date have been somewhat more combat-focused than many of the shows really were. Of course, the fact that the license keeps bouncing between hands and developers (unlike LucasArts, who've been refining their Star Wars offerings for the better part of two decades now) has not helped matters in the slightest.
Sequelitis: it began with the very first episode of Voyager, but by the time Insurrection rolled around, even major critics were noting that the franchise was taking a fairly serious and noticeable dip in quality. Enterprise and Nemesis are "credited" with coming within a whisper of killing the franchise (Nemesis being the only Trek film in history to not turn a profit); the reboot salvaged it, but the quality of sequels to it remain to be seen.