I'm not sure how much of this is "added to" or "going back to" [from earlier playtests] or, maybe even already included...but what I'd like to see...
1. Simple "base/big 4" classes. They were there...and then it seemed they continued to pile stuff on. Now, how much of that was them testing "additional/optional" bits n' pieces and how much was to be taken as "default" I can't really say.
2. Easily added "sub-classes" through backgrounds and "specialities." I should be able, with minimal trouble, to take a Fighter and get a knight, non-"barbarian" berserker, a swashbuckler, hand-to-hand/pugilist/martial artist, professional mercenary crossbowman/axeman, a tribal spear-chucker/javelin user, etc...I should be able to take a mage and with a background or specialty make a rural "wisewoman/witch-type", or ceremonial magic/ritual specialist magician, a barbarian clan's run-caster/soothsayer type, etc...not necessarily an arcane "tradition" in the sense of specialist schools. The illusionists, necromancers, etc... seem easy enough to do and/or easy enough to come later with extended spelllists, splat books, and the like.3
3. A SIMPLE/minimal feat list. Enough options for non-casters to be comparable to casters in player options, but not so many as to invoke option paralysis or require pages and pages of reading just for feats.
4. A SIMPLE/minimal skills list. I'm kinda on the fence as to whether this should include interactive skills (persuasion, diplomacy, bluff, etc...) or not. I suppose these could be included in the expanded "Standard" or "Advanced" game options. Depends on how well they do an interaction sub-system, I suppose. I am prone to want this to be left to roleplaying moreso than not. But we'll see. Honestly, I think more than other elements, interactions should be effected by/based in background...with, then, possible skills adding further bonus.
5. An effective but simple interaction subsystem that still allows/depends on roleplaying [then adding bonuses/penalties on top of the RP element). I would include the Morale system in the interaction pillar of mechanics as it is where, typically, "parlay" moves into combat and/or combat can move into surrender/capture/parlay.
6. A severely pared down spell list...for all casters/types of magic. Adding spells after in supplements, online resources, "Unearthed Arcana" and "Ultimate Magic" hardbacks and such is a no-brainer. Not to mention, we have 40 years of backlog of spells. If there's not something you want in your games in the initial release spell lists, it should take minimal effort to port/convert your favorite spells into 5e terms.
7. A thorough, but easily incorporated, set of guides for stronghold building/realm ruling in the "Expert/Companion" level play...given what we know of 5e, I would put this around the classic area of 9th [ye olde "name" level]-12th level. Obviously, this wouldn't need to be included in the "simple/basic" version of the game, but for the Standard or Advanced I would certainly like to see it. Mass combat/inter-domain conflict optional...as its own separate module.
8. Warlocks and Sorcerers that have good flavor, moreso than kewlz mechanics, that do not make the Wizard/mages lame or inconsequential. IMHO, the Wizards are the WIZARDS! There is a somewhat unspoken implication that they are the masters of magic. Witches, sorcerers, and other arcane classes are just trying to figure things out on their own, steal and/or take the easy way to power, and/or keep up with actual wizards. Obviously at higher levels this isn't necessarily so, but for the beginner/starter PCs, yeah a wizard should be able to "out magic" a warlock or sorcerer.
9. I would like to see an easy to incorporate system for psychic powers/psionics...but I have no idea how/what that should be...nor whether psionic classes need be included out of the gate or if a supplement "Powers of the Mind" module to tack on for those that want them will suffice.
10. Non-"shouty healer" Warlords. Warlords are what? Lords...of War. Give me the battlefield stuff and combat effectiveness, and yes some "leadership/inspirational" skill or persuasion. Mid-combat shout healing, while yes, very handy for winning combats, is just not good for immersion. This seems already in the works, if not the bag, so that's good from my perspective.
I'll reiterate the "randmoness/specific tables" requests as well. But, again, I have plenty of those from past editions so if 5e doesn't have them...I still know where to get them...or can make up my own. Well, on that note, I guess this counts enough to be its own thing...
11. I will add, to the random tables list, an optional "Spell Disruption/Interruption Effects" for casters that don't get their spells off...which I suppose mandates spell interruption mechanics if they aren't already there [even as an optional module?]. Making magic should be tricky, potentally dangerous, theriouth business!
I'm sure there's more...but that'll do for now.
[EDIT] OH! And I forgot to mention...a great big bold, whole page explaining (for those who don't know/just entering the D&D world or never having played this way before) the whole "This manual is full of Rulings not Rules", "Guidelines not Law", and "Saying NO about any particular element in the game is not a dirty word and completely permissible for the DM." I want it at the beginning of every blessed book, PHBs, MMs and DMGs so ni matter what is being looked at/owned/used by the individual players, they all are reminded. Granted the DMGs can go into this with more detail, guidelines, suggestions for incorporating and how to effectively adjudicate and mediate for your group.[/EDIT]