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.
Franchise Original Sin: Most of the faults found Voyager and Enterprise were already very present in the much-lauded middle seasons of The Next Generation, and some can even be found in The Original Series; things like the anomaly of the week, the malfunctioning holodeck, the evil versions of regular characters, the shuttle crash plots, and the B-plots that feel like a soap opera. But it wasn't until later in the franchise that they really started to grate on viewers, since it finally started to seem like the same thing over and over again.
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".
It Runs on Nonsensoleum: Obviously, we have a long wat to go before the science of "Star Trek" could be done in reality...
Mary Suetopia: Roddenberry's vision for Trek, but especially the first season of Star Trek: The Next Generation.
Moral Dissonance: Often comes up with regard to the Prime Directive. Exactly how seriously the Federation (and the protagonists) treats this is often directly connected to how much it benefits their interests, and they have been known to make first contact with pre-warp (TNG "Angel One"), or even pre-industrial (TOS "Errand of Mercy"), societies that happen to be conveniently situated near borders with hostile powers. Somewhat hypocritically, Earth was the beneficiary of first contact (with the Vulcans) prior to the establishment of United Earth purely because an individual scientist and his followers successfully tested a warp drive without government sponsorship during an anarchic period immediately after World War III (Star Trek: First Contact). Not too far into the TNG timeframe the Federation would almost religiously avoid dealing with similar planets.
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.
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. While Interspecies Romance is quite common to the point of being expected, any deviation from heterosexuality is definitively explained by Bizarre Alien Biology. This topic has been much discussed, including on the Other Wiki, Star Trek's own Memory Alpha, as well as other essaysand articles. It should be further noted that shows outside the science fiction genre had main characters that were not heterosexual, both prior to and during the Trek franchise's resurgence during the 1980's and 1990's. Examples include Dynasty, Melrose Place and Dawsons Creek. Science fiction would also enter the game with the introduction of Captain Jack Harkness on Doctor Who, and expanded in the spinoff series Torchwood. The short-lived Battlestar Galactica (Reimagined) prequel series Caprica would also include LGBT characters. But Star Trek has yet to do so except in non-canonical expanded universe materials.