I'd like to echo the sentiment that the only 4th Edition that I'm really interested in is one that is significantly different from 3.5. If it's like 2e was to 1e, I don't know if I would bother with it for a while.
1. One of my greatest desires is for a system that doesn't break down into supplement-itis after the first couple of years; of course this is contrary to what the market seems to want. Carrying around three core books and a setting books is reasonable. If I need to cart around a dozen hardcovers to each game session I run, then it starts to get really cumbersome.
2. The greatest change that I would make would be to cut down the number of core classes. There are too many core classes now, when all of the supplements are taken into consideration, and even some of the PHB core classes are unnecessary. There really only need be three or four base classes: Fighter/Warrior, Rogue/Thief/Expert, and Wizard/Mage/Spellcaster (and maybe Cleric).
The details of multiclassing, the skill systems, and the feat system would need some re-working to accomodate it, but all of the more specialized classes should be able to be built on a foundation of these three (or four) base classes, with the appropriate selection of skills and feats. A Ranger would be mostly a Fighter with a bit of Rogue, and a good selection of wilderness skills and feats, for example. Obviously, you can't quite do this with the way the system works now (well, you could, but it would be a far less effective character than an actual Ranger), but with some re-working you should be able to. Prestige classes could be a part of the system -- but with much more regulation. Some specialized roles lend themselves easily to a prestige (advanced) class, like a Paladin, which should feel like an actual Champion of Goodness, rather than a Fighter with watered-down Cleric abilities.
3. I would like to see the tenuous distinction between arcane and divine magic dropped once and for all. It gets less and less significant with each edition. Cleric spheres in 2e and domains in 3e give access to a great number of spells which were once the sole province of Wizards. The main guiding principle now is "Wizards can't heal," which still doesn't make any sense.
The only real reason for Clerics in D&D is so that PCs can be healed. Any character can be a devout follower of a deity. Any Wizard can cast spells in the service to his or her deity. Any Fighter can smite foes in the name of his or her god. Clerics get stuck with the role of providing the necessary healing to the party, and since that would be a really boring task for any sort of long-term play, Clerics get all kinds of extra abilities, decent BAB, decent hit points, a good selection of armour. If a Cleric were just a Wizard who could cast healing spells (ie had crappy hit points, crappy combat abilities, and crappy armour selection), nobody would want to play one.
The solution? Reduce or eliminate the game's reliance on magical healing. If characters didn't have to be continually healed by magical means, then Clerics wouldn't be as necessary. Unearthed Arcana provides some alternative systems that partially address this issue -- armour as DR, armour converting damage to non-lethal damage, wound and vitality points, damage saves, etc. But none of these options are part of the core system, and none of them really give enough consideration to the bigger picture of the game as a whole. Part of the issue is in the inflatable nature of hit points... when your 10th-level Fighter has 100+ HP, it takes ten days of complete rest to heal. Or a good ten castings of Cure Light Wounds. Or more powerful healing magics. The current (and historical) damage model of D&D requires magical healing in order to avoid the game grinding to a halt while the party recovers from every encounter. And if this isn't as much of an issue, then the game doesn't really need a Cleric.
And if you don't need so much magical healing just to survive a typical adventure, then it makes it easier for those who want to play a low-magic game to do so without having to make drastic changes to the rules.
4. Cut the distinction between class skills and cross-class skills. All this really does is heap an extra penalty on the classes that get fewer skill points, as they invariably have the shortest lists of class skills. Plus, it makes bookkeeping and NPC generation a real headache, because you can't just start with X number of skill points and select your skills; you have to consider the order in which levels in different classes were gained. This takes way too much time, and is very prone to errors.
5. Get rid of Gnomes. In over 20 years of gaming, I've personally seen a total of one Gnome character. YMMV, but it's always been a pretty unappealing and redundant choice to me. Pick a dwarf or a halfling and quit sitting on the fence. Either replace it with a more interesting racial choice, or just (god forbid) don't have as many choices of character race.
6. Re-work the magic item creation rules. The pay-XP-to-craft system doesn't really make any sense, in terms of the game world. Crafting an item, if anything, would be a learning experience and one would think that you would actually gain some XP from it. Perhaps require some exotic materials (instead of just a gp cost) that may involve a quest. And create a new classification of item types that isn't lifted directly from 1e and 2e, because the whole "Wondrous item" category is very poorly thought-out. Why bother waiting until 12th level to take the Forge Ring feat to make a Ring of Invisibility when you could just craft a Wondrous Item, say a pair of Earmuffs of Invisibility, at around 4th level? Ugh, the system is just full of holes when I start thinking about it.
7. Include rules for levelled weapons (and other items) in the DMG, a la Weapons of Legacy, Unearthed Arcana, or a Dragon article that I can't remember which issue it appeared in. Provide a handful of examples.
8. Provide guidelines and/or alternate rules systems (or methods of scaling up or down) in the DMG for running games with a different tone than the standard D&D rules assume. What is a world like where magic is commonplace? What would a low-magic setting be like?
9. Create a new "default" setting for D&D that isn't Greyhawk, Forgotten Realms, or Eberron. It doesn't need to be a large setting, perhaps just a small area of a continent (like the "Known World" of the B, X, CM sets) that can be fleshed out or just used for inspiration. The setting should take into account the logical implications of the assumptions made by the base ruleset -- which is why Greyhawk shouldn't be the default setting.
10. Give the spell system a bit more flavour. This is something that has been lost since 1e. The Druid spell list was very different in flavour than the Cleric list. Illusionists had a very different spell list than Magic-Users; many of the most powerful illusion spells were not even available to general Magic-Users, and most illusion spells were accessible to Illusionists at a lower level. Specialist Wizards in 2e and 3e are realy bland, and even general Wizards suffer from a lack of flavour, with their "kitchen sink" approach to spells. There is a lot of crossover in spell lists now. Perhaps have spells acquired along a specific "path" in which more powerful variants of a spell cannot be learned without mastering the preceeding spells. Should you suddenly be able to learn Summon Monster III without having even practiced the basics of Summon Monster I? Shouldn't Burning Hands be a logical predecessor to Fireball? Or maybe spells themselves should be more scalable. Or have the base "Wizard" class be more of an apprentice or generalist, and only members of specific prestige classes (such as a "Grand Illusionist") are able to cast the most powerful spells of any given specialized field of magical study.
I'm sure that I could think of other wishes for a 4th Edition, but these are the first ones that come to mind. A lot of things could be streamlined, and there are still quite a few mostly-redundant classes, spells, feats, skills, etc that could be eliminated with a more flexible approach.