Realistically, Star Trek isn't the way to address these things. At this point, without a pretty severe reboot, it's probably not going to happen.
Some things that I think Star Trek could address:
AI and the technological singularity
Lots of super smart AI were shown, so why were they unable to create smarter AI? Ignoring silly predictions based on Moore's law, Data was smart enough that he should have been able to create a more stable version of Lal, who in turn could have made an even smarter being. If this wasn't a possibility, then they should address why
Certainly this is addressed to a degree with Khan. But the supermen were only genetically engineered for strength and intelligence. Other things we should see would be drastic reduction of aging, hair loss, obesity, and disease. Another thing worth considering is the whole mechanical aspect. Someone mentioned Geordi should have been more the norm than the odd man out. There's certainly a larger possibility for cybernetic implants.
Increased brain knowledge and devices that support this
This might be part of the transhumanism, but there is research being done today to suggest brain activated computers. Whether it's something as clunky as a VISOR or more discreet like contacts with a HUD. People are going to need to have better access to their devices. And in general, there should be no secrets about the brain. I find it more likely that we'd figure out the brain before we'd be warping around the galaxy. Things like Picard having Irumodic Syndrome shouldn't really be an issue.
It's possible that Star Trek already uses this. They've always been purposefully vague when it came down to this sort of thing, but I don't think it would hurt to mention quantum computing, maybe even as something that's outdated. Things at least need to move away from the isolinear rods and such. Voyager at least had a start toward this with the gel packs.
If they're not using devices that actually enhance the organs, they should certainly be into synthesizing organs for surgery. Picard should never have had an artificial heart and blood should have been able to be easily created. And the surgical methods should be far cleaner or less invasive. Transporting a fetus was a pretty wild idea. You have to wonder what other medical applications there could be.
There's probably a lot more that could be here.
And in general there is a large problem with these that you might have already seen. A lot of these make existing stories not possible. While they may be opening up doors for new science fiction style stories, they're closing the door on us being able to identify with the characters.
To be realistic, the future in a few hundred years should be scary and very foreign. As someone from 1712 would probably flip out if here today, we should probably flip out in 2312. That takes away from the general idea of Star Trek where everything is more or less the same as today, just with all sorts of cool technology and socialism that somehow works. The people who showed up in "The Neutral Zone" weren't really that terrified because the people were like those in the 80's just placed in a fantasy future setting.
Audiences don't really care about what it ought to be or if it's really hard science fiction. Star Trek has always been very light, and they might throw some plausible sounding science words in to make it seem believable, but ultimately it's not the franchise that's ever going to care about such things.