Well, let me state that I am currently DMing a 1e Greyhawk game, and the players and I are enjoying it quite well.
What don't I like about it? Well, let's see (note much of this is personal pref, not so much issues with the system, per se:
--Rangers in Platemail casting magic missle - doesn't fit my idea of a Ranger.
--Bards - should have been their own class
--Monks - can't put my finger on it, I just hate 1e monks, always have.
--Psionics - just read it sometime - even Gygax himself hates it.
--Weapon speeds and AC adjustment - again, even Gygax dislikes these
--No save for sleep - makes it way too powerful at low levels, IMO.
--Just about everything about the new (at the time) classes introduced in UA - munchkin city (note: I should really give them a spin again, but I have such a bad impression..)
--One spell at first level for Magic-users - sure, it's supposed to be a balancing factor, but I think it's bit too harsh.
--Initiative "system" - if you try to do it simple, by the book, why have segments? Trying to reason it out, is too much of a pain in the butt. (and I have seen Scot Gregg's explanation, it's quite thorough and well done, but I needed that in 1983.)
--Segments used to really get on my nerves, but now, not so much.
Most of these issues have been alleviated in my game in tried and true 1e fashion: the house rule. I have two variant ranger classes, give MUs bonus spells just like clerics (using INT, of course), disallow psionics and bards, have my own init system, etc... back in the 80's, when we were confused, we'd fall back to what we did in the Moldvay basic set.
Oh, and for those of you who were griping about the save/combat charts, Lakofka had an article in Dragon, wherein he consolidated them into two tables, one for saves the other for combat. I've recreated them in excel, and they now fit on one sheet. if anyone out there playing 1e would like them, PM me.
Now I'll sit back and wait for the flogging from both 1e and 3e fanboys......