The first thing that bugs me about Star Trek is the music. I'm not talking about the theme music or background music. It's the music they depict Star Trek characters listening to or playing for entertainment. In all the series (that I've watched) & the films, they depict the characters listening to or performing Classical or Jazz. I don't have a problem with either of those forms, but I prefer Rock, Metal, or some Pop music. None of the characters is ever seen listening to or performing Rock, Country, Blues, or even Folk music.
In the few instances that Rock or Pop music has been heard in an episode or film, it's always either some sort of galactic hippies (in the original series), or in the past (the First Contact film). It seems to imply, to me anyway, that those forms didn't "survive" or aren't "proper" in that present. It's like it doesn't matter, like it's not allowed. In First Contact, you can see that when Efrem Cochran plays his rock music, that most of the Star Fleet folks seem to act like it's a dentist drill. Granted, one part they dislike about it is the volume, but even after it's turned down, it's still seen as an annoyance. Then there's been no Country music that I've noticed. No Hip-Hop, no R&B, no Soul, no Funk. Especially no Latino music, salsa, rumba, bossa nova. It's not right & should be addressed.
Second, is depicting real diversity. Of course the aliens (Klingons, Vulcans, Andorrans, Romulans, Ferengi) are diverse. However, when depicting people of Earth, though they are racially/ethnically diverse, they don't depict people wearing yarmulkes (Jewish), or kufis or other Islamic clothing. It's as if the whole Earth is one homogeneous religious mass. Why? I understand that the shows/films aren't about religion, but the people of the future would still have religion & practice it.
Finally, is the depiction of dissenters. In the Star Trek universe those dissenters are call Maquee (which I've probably misspelled). The Maquee don't believe Star Fleet offers a utopia; they think it only enforces conformity. It seems they are right to a point. People who don't want Star Fleet are considered outlaws. They aren't just left alone; they're arrested. It just seems wrong to me. I will agree that at least the series/films acknowledge the existence of these dissenters. However, they don't seem to be thought of as having any valid points of view.
I'll still watch Star Trek in reruns & films, but I'll always be aware of these "omissions" while I'm watching.