If you don't mind, what in your opinion are these core issues?
General bonus progression (to hit particularly, but others are relevant as well) is a big one. Right now 4e assumes it will come from a number of sources, half level, ability score, and enhancement at the very least. Several questions beg to be answered here:
Is it necessary to have an ever increasing to-hit bonus at all? In many respects I don't see that this actually works very well. It forces the game into a 'treadmill' format for one thing. This was primarily intended to provide a sense of progression, but is it really doing that very well? Is it necessary or are there already other good ways to accomplish this? In other words what if you just blew away all progressing to-hit bonuses? Monsters would still have increasing damage output and hit points. Low level PCs would have SOME increased effectiveness against higher level monsters, but you'd still have plenty of scope for increased threat level. Defenses would obviously no longer progress either, but higher level monsters could still certainly have somewhat increased defenses (and to-hit as well for that matter). You would now be free to provide things like enhancement, feat, etc bonuses as genuine rewards to the character. A +1 sword would forever be an advantage of the same degree throughout the character's lifetime for instance.
The same issues arise with ability score bumps. They channelize characters into narrow specializations in a rather artificial way. The fighter cannot be a decent bowman because his crappy dexterity (even if it starts good it will soon be crap compared to his ever increasing STR) means it isn't a viable path. There are work arounds like some feat patch or alternate sets of STR based powers to use with a bow, but they have their own disadvantages.
Again this rears its ugly head with skills. If skill bonuses were simply absolute values that didn't increase with level then certain issues people have had with the skill system go away. Again it allows characters a broader range of abilities that remain relevant throughout their careers. It also kills off the vast majority of the growing gulf between the best and worst skill bonuses as levels go up. It would open up skills working vs defenses in a much more equivalent way to attacks, which again fixes several awkward little problems and opens up more design space.
Many other issues suddenly go away as well, such as the dichotomy between heavy and light armor and all the subsidiary issues with non-dex light armor classes and the need for various feats and class features that patch up that mess. The armor system is also simplified with no more need for 'masterwork armor' or the uneven armor bonus increases of Essentials (which is basically the same thing). Again an enhancement bonus becomes something that remains relatively advantageous throughout the character's lifetime.
Combat is nicely tactical and in many ways elegant, but the system is overcomplex in ways which haven't really panned out. There's no need for the level of complexity of immediate action types and OAs for instance. This stuff could be substantially streamlined. It would impact a lot of powers and whatnot but presumably the power system would evolve to match.
Powers themselves are a large mess IMHO. The level of distinctions were too fine-grained. This has led to a plethora of powers which deploy a vast array of very similar but not identical effects. In play they really aren't all that distinct except in terms of fluff. A lesser number of power choices with greater distinctiveness between powers and specific types of effects more restricted to specific power types would make more sense, be vastly simpler on the players, provide the same degree of tactical flexibility, and move a lot of build distinctiveness that is now forced into other elements back into powers. This would make it easier to build out specific concepts as they would be much closer to just 'pick this and this power' vs the need to plan which 5 feats etc you have to juggle into place to make your concept work. This would be a great easing of the design burden on developers too and lower the bar to new content.
I could go on. None of these things are really serious issues with the 4e engine CONCEPTUALLY as a straight d20 based roll-high combat system or the basic concept of defenses, saves, conditions, structure of the tactical game, etc. They are simply issues that arose organically out of the details of how that engine was implemented and which have had negative impacts on the rest of the game. I think this is basically due to the fact that the game was a fairly new design and the developers couldn't easily see what the impact of each decision would be until they implemented it, at which point it was very hard to go back and change those decisions since it meant reworking everything else on top of that. So the core engine design froze pretty early on, and everything else had to work around the lumps.
Notice too, EVERYTHING I propose is almost entirely subtractive. Subtractive changes to the game are not really possible using an exception based system of extension design. 4e is great, but it does a few too many things. Simplifying the core engine by 30% could turn a very good game into the RPG of the century.
