Great thread. I love conversations like this; as a DM who likes creating his own worlds this thread is a great starting point for designing the foundations
of a cosmology (which should be, in my opinion, the first place to start in the nitty gritty of setting design).
What this thread has clarified and solidified in my mind is the thing that has always bugged me about religion in D&D: it has never seemed to be what it could (or maybe should) be. It seems as if it has always been a tacked-on way of having a class that can quickly and easily heal the heroes (and I am referring to the TSR/Wizards treatment of the subject - plenty of examples of third party depth in this respect).
Hmmm, let me refocus by quoting the original post:
What features of real life religions couldn't apply to D&D religions?
What features probably wouldn't apply?
In what ways would (or could) D&D religions mirror real life religions?
There are no wrong answers, or at least I don't think there are.
Your thoughts?
Let me first say that any answer to these three questions will depend on how one perceives two things about D&D religious canon (and these two things have, of course, been brought up already - I'm collecting my thoughts

);
1. How powerful is the deity?
2. How likely is the deity to intervene or exert control in the setting? This will of course be dependent on the first point.
These two points have, to a great degree, been left up to the DM by TSR/Wizards, though point 2 has been given more attention and clarification than point 1. Having said that, and in regards to the core settings - FR, GH, etc., these settings have fallen woefully short in giving their religions the attention they deserve.
So to answer, in a general way, the original post:
To question 1 - NO feature of real life religion would not be able to be applied to D&D religions; even atheism, or non-belief, is a religious standpoint. In real life it is simply a refutation of everyone else's view - and as such is based ON everyone else's view, and is therefore a part of the religious spectrum. In a fantasy setting non-belief could be viewed as either insanity, ignorance, or principled stubbornness.
To question 2 - This seems to me an extension of question 2 (since I think ALL aspects of real-world religion are applicable to D&D - D&D is, after all, a product of the real world), yet I'll take it as a question that focuses in on the concept of faith. I could just say "see above", but I'll tackle it like this: yes, faith could be an integral part to a D&D setting. Even though faith is belief in something that isn't provable (except to oneself through personal experience), and in D&D the gods are provable, and therefore faith would seem to be killed, it could still play a huge part in the setting's religions. It depends on how the DM wants to run it and even more on how the player wants his character to view religion - ala Col. O'Neil - "Just because you wield incredible power and call yourself a god, that doesn't mean you ARE a god". The ultimate definition of godhood springs from the worshiper, not the dude claiming to be a god. So all the "gods" listed in the FR campaign guide are just posers; the real God(s) is(are) above and beyond them... but I can't prove that.
To question 3. Oh god, um... I think D&D religions could and should mirror all aspects of real-life religions; I mean, can you think of any aspect of life that at least one of our religions hasn't tackled? Nothing comes to mind for me... except maybe... nope, nothing.
But to return to the idea that D&D has neglected the incredible power and influence provable gods would have on a world...
I mean, come on, these are GODS here. Even if the good gods prefer a hands off approach to the world, the evil dieties will force them to exert control or stand by and watch while they take it all over.
I suppose the point I'm rambling towards is that in a fantasy RPG setting where incredibly powerful gods (or as Jack O'Neil would say; Snake Heads) are REAL, ... ALL cultures would be ruled, in one way or another - depending on the level of Lawfull-ness or Chaotic-ness of the god (and NOT by said god's level of evil-ness or good-ness) - by the churches and religions of that setting. Rulership is about politics, politics is about power, and the greatest power, in a fantasy setting, is god(s).
It seems to me that the only way a setting would have religion NOT be in the supreme rulership position is when the evil deities are of sufficiently lesser power than the good deities that the good guys can take a hands off approach (which seems to me to be one of the core priniples of goodness: allowing a person to make their own choices and at the same time protecting them from those who would take that right away from them).
Hmmm, this leads me to think I might house rule my setting's alignment system to:
Lawful Neutral
Lawful Evil
Nuetral Good
Chaotic Neutral
Chaotic Evil
Hmmm...