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.
As an alternative view, Janeway returned, the wormhole reopened, Bajor is a powerful and prosperous Federation member, a second more advanced Deep Space Nine replaced the lost one, the same devastating conflict in Destiny also liberated the Borg and freed billions from oppression, and in doing so removed the biggest blight to Trek 'verse civilization, the Federation has held together, rebuilt and reaffirmed itself in spite of everything, and inspired the Typhon Pact nations to start to overcome their histories of xenophobia and isolation on top of that, the Andorians are cured of their genetic problems, the Cardassians and Ferengi have the best governments they've ever had and are now official allies of the Federation, the Romulans have a moderate and diplomatically adept government, the Federation has slipstream drive and is penetrating all four quadrants, and Starfleet is starting to turn back to exploration again. Also, political instability and uncertainty isn't, others might say, anywhere near "Crapsack World" - especially when war has been consistently avoided (Borg aside, and they're more a force of nature than a nation).
President Nanietta Bacco, who went from a "the president resigned last book so we need a new president" character to a popular character carrying her own West Wing-style political novel, Star Trek: Articles of the Federation.
Fridge Logic: One of the more infamous is the desire to make sense of the Tamarian language from Darmok. A very popular episode, but great amounts of Fridge Logic result, for the books to eventually deal with. For example, how do the children learn the legends? Answer: Probably not unlike how Chinese speakers learn the four word idioms. English too has plenty of strange expressions with obscure origins, but speakers understand the meaning from the context. In fact, the metaphorical meaning tends to become the ordinary meaning over time; for example, English "understand" no longer refers to standing under anything but has become a dead metaphor. Or perhaps the children are taught the stories via some visual medium, like movies or plays.
Fridge Logic #2: To build starships, one needs language more precise and less ambiguous than metaphors. But this too is all explained in the Star Trek Novel Verse. Tamarian mathematical and musical notations are very closely linked. Tamarian engineers and programmers sing equations, transferring instructions through music. Even in ordinary speech, numerical information can be conveyed through the pitch of a Tamarian’s vocal harmonics, though it can be hard for untrained Human ears to discern the nuances, just as it can be hard for an English speaker to learn to hear Chinese tones.
"This answers the infamous question one linguist posed to illustrate the apparent limitations of Tamarian as a practical language: “Mirab-his-sails-unfurled factor what, sir?”
Fridge Logic #3: Why the universal translator even translates their language in the metaphorical way in the first place, when we know the UT works on some kind of technological telepathy. If when they say "Darmok and Jalad at Tanagra" they mean "alliance", then why doesn't the UT just translate it as "alliance"? Answer: It wouldn't work in real time. "Computer: Cross-reference: Darmok, Jhillard, Tanagra." Computer tells the story, they go "Ah!" This would resemble the footnotes commonly seen in anime subtitles (see case 3A under Translation Style Choices). But explaining Tamarian legends to a foreigner is a slow process. And besides, it loses the more subtle information about what kind of alliance is meant: in Tropese, it'd be close to Enemy Mine.
It even loops right back around to Fridge Brilliance: English "set" has over a hundred meanings distinguished only by context, and Mandarin Chinese can be just as bad with its homophones and four-word idioms. Likewise, there's so many possibilities for a particular Tamarian phrase, it requires an incredible intuition to determine the intended meaning, one normally honed through a lifetime of speaking such a condensed form of language. The universal translators are notorious (Depending on the Writer or perhaps the make and model) for having difficulties with some of the more 'quirky' or abstract parts of languages.
Mary Sue: Sonek Pran of A Singular Destiny, so very much. Exotic racial background? He's actually 1/4 Human, 1/4 Bajoran, 1/4 Betazoid and 1/4 Vulcan, plus he has the distinctive Bajoran nose, Betazoid eyes and Vulcan ears. Crazy connections to other characters? He's been an advisor to many Federation presidents, and the Empress of the Imperial Romulan State knows of him somewhat through his reputation as a folk musician. Uber-skills? Why he's the only man who can negotiate tricky situations and he serves as the mentor to Ezri Dax.