For my own self, and I know many will find so much to criticize about this:
4e was a great structure presented badly. 5e actively tried to avoid anything that smelled like 4e, to the point of repeatedly reinventing the wheel, sometimes completely unnecessarily (e.g., 4e crits are just flat simpler and easier than 5e crits.) So, bring back more of the engine of 4e, but disguise it. D&D: Mojave, as I've previously phrased it.
Vancian casting needs to be reworked. The old 4e ritual system was a good try, but probably needs to be tweaked further. Perhaps Wizards get bonus "utility" slots or something? I dunno. Something to signpost this better. But variable-encounters-per-day vs fixed-powerful-resources-per-day still isn't working, and something has to be done. The kludge of Legendary Resistance and the like is a very simple proof that Vancian casting is simply too powerful as it is.
Monster design has already drifted in a 4e-like direction with 5.5e, and I expect it to drift further.
Some real thought needs to go into non-combat stuff. Not necessarily "mechanics" per se, but...something. Because as it stands, as far as rules go, anything that isn't combat practically doesn't exist unless the GM does all of the heavy lifting, and that's not tenable as a long-term design element.
Terrain needs to be made more important, and ideally, forced movement as well. That's one of the great things about 4e, and 5e pretty much totally erased it, which encourages really really really dull combat environments.
Simplicity vs complexity needs to be distributed better amongst the class archetypes.
Entirely opposed to what several posters have said, I think 6e needs several more classes. Up to 12 more than 5e has. Replacing those with "talent trees" is absolutely not going to achieve the results folks would like to see, and will instead just make things harder to understand and even more build-focused than they want to see, especially because balancing talent tree type things is significantly harder than balancing separate (sub)classes that can't easily mix.
Finally...for God's sake, give us well-made Novice Levels and incremental advancement rules. This is genuinely the single greatest step that could be taken toward making a D&D that is actually a "generic" system that serves everyone's interests. I am not joking, it is legit actually something that serves nearly everyone. It serves the hardcore simulationists, because such usage helps take the edge off the awkwardness of discrete levels, and makes characters feel more like they "build up to" their increases in power. It helps the old-school/high-difficulty fans, who want to spool things out and start extremely minimalist. And it helps the gamists of all stripes, because it means 1st level can be actually competent, rather than a training-wheels session, and they can elect to choose what advancement rate best suits them. Literally everyone wins, except the designers needing to do the work to make it happen, I guess.