You know, this thread has been very educational for me.
It's done two things:
1. Clarified why I dislike elements of 4e.
2. Clarified how those elements can still be good.
I notice that the things I don't like about 4e are the "gamist" elements that pull me out of the moment and emphasize "this is a game." I think 4e is fun, but I have trouble maintaining immersion.
I don't like: how healing is done in 4e, forced movement, weird stuff that triggers off of seemingly unrelated things, minions as they're done, marking, in combat versus out of combat specifications and some other things that make it really feel "gamey" to me as presented.
Before people get upset at me for getting all negative, there's a pretty big but coming.
BUT each and every one of those are great ideas if they had balanced gamist with simulationist, and some people have mentioned in this thread how those things could be toned down.
Healing: I love fully designating HP as separate "engery points" rather than hit points, as Herreman Suggests. 4e does this, but blends it with wounds as well. Right direction, but not far enough here, I'd say.
Forced movement: much better than the only real option in 3e of bull rush, but again, needs to be toned down, as mentioned by others. If it were to only happen when I were next to someone, it'd feel much more real to me.
Weird stuff that triggers: I love the idea mentioned of "I do x and y AND z happen". I love anything that involves other players when it's not their turn. I dislike it when "I hit that guy, you heal 5 damage" where hit points still somewhat represent wounds or "I hit that guy, you get to move". If it makes logical sense, then I'm all for it. e.g. "I hit this guy you're flanking me with, you get an attack."
Minions as they're done: a lvl 20 minion should be a MAJOR threat to a level 1 character. It should not have 1 hp. Minions are a fantastic idea, and I love them as done at lower levels. Why not give level 20 minions, say 1/4 of the hp of other baddies of the level, or 1/10th? Just give them few enough hp that a character of that level can one shot them.
Marking: Again, I like it, but too "gamey" for me. I like the idea of taunting enemies and also the idea of being able to harry them (harrie?). I don't like it when it is explained simply as "marking" without an obvious roleplaying mechanic or reason, and how the same mechanic requires different descriptions in different situations. (I taunt Joe the orc, I tempt the ooze into attacking me).
In versus out of combat: Some things make sense for this, like rituals. However, I don't like that many of the in combat things don't (or at the least, don't seem to be written) so that they can be used out of combat. I'd like more clarity on that. e.g. if I have a freezing blast attack, can I freeze water with it? Can I chill my ice tea? Can I freeze part of a lake? A bathtub? Etc.
What I dislike most about 4e is powers, specifically that they seem written for combat only. I do like the idea of cool at will, encounter and daily balance. I hate it as a roleplaying convention. Nothing in the game breaks my immersion so much as this. However, I think there's something to it.
First, it would have to be more carefully addressed. It's easier with magic, but the whole "the fighter can only do this once" deal needs to be carefully written so I can understand WHY he can only do it once. Herreman's hit points would be useful here...rather than once per encounter, it might cost hit/energy points...so you only want to use it once or twice before you get to recharge energy. You CAN use it more, but you'll be knocking yourself unconscious to do so.
When it comes down to it, 4e has some really neat stuff in it, but there was a decision that the rules could be divorced from the fluff, and that people would make up their own fluff at each moment. This is a feature (rather than a bug) for some players of 4e. I think it went too far in this direction, and it also allowed for designers to envision rules that take some serious effort to describe in a roleplaying sense. If I'm spending time at the table trying to figure out how I just did what I just did, I'm pulled out of the game.
So, my epiphany is that I actually like a lot of the skeleton of 4e, but not the flesh...and some bones would have to be broken and reset, but I could potentially like a 5e based in large part on 4e. That's a surprise to me.