#1: The dying mechanic is difficult to reconcile with non-magical healing. My character is reduced to zero hit points and falls down, bleeding out, mere seconds away from death; well and good. But then the warlord yells at him and he snaps out of it and jumps back up, carries on adventuring as if nothing had happened, and is fine the next day? This is the place where the hit point abstraction breaks down IMO. Even with magical healing, you'd think there would be some effect from being on the brink of death.
I don't have a problem reconciling this. It's up to the DM to put a narrative spin on it.
I wouldn't describe such a situation as the PC being "fine the next day" as if nothing had happened. He is very much beat up, covered in bruises and cuts, and possibly suffering from sprains or dislocations. However, during the course of the adventure, he's running on adrenaline and pushing himself to his limits to accomplish what he needs to. Nobody can carry on like that for long, and he's certainly going to be in a lot of pain once he actually stops to truly take a break. In game terms, spending a few healing surges or taking an extended rest gets him back to full capacity right away, but he's struggling through sheer force of will to put the pain and fatigue aside until he can afford to take a rest.
The DM can describe how the character is feeling, but I don't think it is necessary to apply in-game penalties unless this sort of thing is going on for several in-game days in a row. When the adventure is over and the next one is beginning, the DM can just tell the players that the characters needed a week or two (or a month, whatever) to recuperate and tend to their injuries before setting out again.
If a character is unconscious and near dying several times in the span of a couple of in-game days, I don't see a problem with the DM saying that the character will "recover" after an extended rest (in terms of being able to deal with an emergency should it arise), but that he needs to rest for a few days before setting out on another full-scale adventure. The game doesn't need hard-and-fast rules for this, in my opinion -- just a dose of common sense.
#3: There's no such thing as long-term injury. I don't want PCs to have to deal with lasting injuries all the time, or even most of the time, but I do want it to come up once in a while.
I don't think that most players would find it unfair if the DM applied a minor short-term penalty in exceptional circumstances. For example, if a character is very unlucky and takes a critical hit for a lot of damage, which bring him below 0 hp and into making death saves, on a couple of occasions in a single adventure, the DM could tell the player that his character needs two weeks of bed rest to allow his injured shoulder to heal; until he is able to do so, the character suffers a -2 penalty to his Strength (or directly to hit/damage/checks, etc).
I don't have a reference handy, but the DM could re-skin a disease with the appropriate effects and apply that to a character who has suffered grevious damage in combat and has been very close to death.
#4: Some powers inflict hit point damage that really should not do so, e.g., the bard's Vicious Mockery power. If it does hit point damage, that means it can kill. Vicious Mockery should not be able to kill. (Yeah, yeah, I know, it's magic Vicious Mockery... a wizard did it.)
If all of the damage came from a power like that, it would be pretty hard to describe convincingly. I think it would be more likely that at least some damage was physical, even if the Vicious Mockery was what pushed the character over the edge; he simply lost the will to keep hanging on at that point, or he realized that his previous injuries were far more serious than he originally thought.
For #6, make it much harder to impose the unconscious or helpless conditions; balance those conditions as if they were instant death effects. Then make the coup de grace vastly more lethal. Something like: "The victim is reduced to zero hit points and must immediately make three death saves."
I don't remember the exact wording of the rule, but you could make it so that the coup de grace only applies during combat. Once outside of the immediacy of combat, a helpless or unconscious character can simply be killed (or have to make a death save or three).