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?!
SF Debris believes that Roddenberry's vision of Trek seems to be that in the future, Earth is a Marxist dystopia ruled by Pod-People. Stardestroyer.net has a similar argument in a bit more depth.
Although this in some ways implies a degree of Fan Dumb. While it is true that the series (focused as they are on Starfleet) do not show much of civilian lifestyles in the Federation, what we do see actually implies a rather high standard of living, and quite a diversity of lifestyles, especially when the colonies are factored in. For example, Beverly Crusher's grandmother lived on a colony where everyone was basically doing LARP of life in the pre-industrial Scottish Highlands (with hidden technology maintaining things like the weather). So there is a definite absence of stereotypical Marxist conformity. If anything, people appear to cluster in "lifestyle communities" that meet their personal preferences.
The theory that The Federation is actually The Empire, simply using the Benevolent Alien Invasion to gain new members and extend it's own power. Some point as evidence to in Insurrection, they are recruiting races who've had warp for only a year simply to serve as Cannon-Fodder for the Dominion.
This may very well be a case of Truth in Television though. A common argument floated by anti-Trek commentators is that this future society is so bored and jaded that they have nothing better to do than live out fantasies in holodecks rather than going out and doing anything interesting themselves. However, in real life, early 21st Century America, many millions of people obsess over television, movies and the internet. People fixate on watching sports they do not actually play themselves, immerse themselves in fictional media, or (for those seeking a little more verisimilitude), turn to so-called "reality TV" to watch other people who apparently have more interesting lives than the viewer does.
Base Breaker: Lots and lots and lots of them, but most famously Picard / The Next Generation vs Kirk / the original series, which has entered into Pop-Cultural Osmosis.
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.
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 and its sequel received very good, but not as great reviews than its predecessor.
The films are famous for going back and forth (see Star Trek Movie Curse.) The series, however, follow a much more consistent path. The Original Series was something of an uneven novelty, thanks to inconsistent writing. Next Generation was considered an Even Better Sequel. Deep Space Nine was "different, but still good."Voyager is where the franchise started to unravel, and Enterprise is where it finally came apart.
They Just Didn't Care: The first year's worth of the original Gold Key comic books, done by people in Europe who never saw the show yet were hired to draw and write the book. One horrific example has some guy named Captain "Kurt".
There were also the Power Records comic book/record sets, one of which featured a white Uhura and a black Sulu, complete with a fabulous 'fro. They were recognizably drawn based on the actors, but then altered in the coloring phase. This wasn't so much lack of research as lack of clearance for the actors' likenesses, something which famously got them into trouble with Leonard Nimoy.
Children seen to be somewhat indoctrinated that joining Starfleet is a good thing. When Jake and Wesley decide to do something else, Sisko and Picard seem shocked and unable to conceive of what else it could possibly be? Though that might just be parental figures wanting their children/children surrogates to follow in their footsteps. Picard's own father opposed his decision to join Starfleet, wanting him to tend the family vineyard instead.
Since the Federation appears to be a virtual stratocracy in that Starfleet is often depicted as having broad powers over both internal and external Federation affairs a career in Starfleet could be treated as path for the ambitious, much like the cursus honorum of The Roman Republic. On numerous occasions Starfleet officers are shown exercising diplomatic, judicial and political authority. Senior Starfleet officers may even commit or authorize actions that could put the Federation at war with other space nations! It is virtually unheard of for Starfleet personnel to be subject to any civilian oversight within the Federation, instead being solely under the authority of Starfleet Command. Thus a career in Starfleet could be seen as placing one within an elite social class relative to civilian citizens of the Federation.
The Prime Directive becoming dogmatic. Eventually it seems to be used to freely justify letting people die, under the bizarre logic that evolution has selected people to die and that saving a race could potentially lead to the rise of a new Hitler. Even though if they didn't help, everyone on a planet would be dead! Made worse by the fact that the Prime Directive is sometimes officially disregarded in the case of planets that do not meet the required technological threshold for contact, but which are strategic to Federation interests (e.g. Organia, Angel One, etc.).
The general reaction of non-Vulcans to Vulcans. Vulcan characters from Spock to T'Pol are always getting hassled for not being emotional, no matter how many times they explain their very good reasons for their unemotionalism. Even when their controls are removed (which happens to every main Vulcan character at least once in their series) and their actions prove why it is necessary for Vulcans to put their emotions under so many controls, everyone keeps trying to prod them into laughing or getting mad or whatever. Granted, some Vulcans do lord their logic over their emotional colleagues, but they get this even when they're minding their own business. So much for respecting other cultures, eh?
Heterosexuality is virtually universal. Exceptions to this are rare and always involve alien species in some way. Even bodiless Energy Beings seem to have gender identities and are depicted as heterosexual. Q jokes about appearing to Picard as a woman, but never does so (although he appears in nonhuman forms several times). He also has a long-term (billion year) Q "girlfriend", with whom he has a son who is a stereotypical heterosexual horny teenager that is obsessed with females even from the "lesser" species.
Human gender roles and culture have not changed much over the centuries. Wives still commonly take their husband's surnames with only rare exceptions. Female Starfleet officers tend to either be One of the Boys, or else The Chick, with no middle ground.