I find a great deal to love in the latest edition of D&D. True, it doesn't have the rough charm of the Basic D&D games I used to play, but that's as much to do with me changing as the game.
There are some things I don't bear a great love for, but have learned to accept: the sheer power of high level characters (I keep reminding myself that high level characters are Aragorn, Luke Skywalker or Achillies, rather than Fatty Bulger, Red Six, or 2nd Gravedigger. They're supposed to be powerful, and not supposed to be scared of bandits with crossbows.), the proliferation of magic items (again, great heroes in literature tend to have suitably epic accoutrements, although not to the same extent.), and the whole magic item economy. All of these are less than ideal, but I think they're features, rather than bugs.
However, there are two key areas which I hate about D&D. I think they're probably known to the powers that be, and are likely to be slowly addressed over the next few years, or in the next edition:
The biggest problem I have is that the game takes too long to prepare. There are a huge number of tools available for the DM in preparing adventures, in the form of monsters (& templates), sample traps, adventure ideas, and so forth. However, using a lot of these tools requires a lot of generation of stats, many of which won't even be relevant to play most of the time (but, when you need them, often you really need them, and I find winging these things to be a bit grating). Really, if I want to create a 12th level Orcish Barbarian/Rogue/Blackguard, I have to go through quite a lot of pain to do so. Add a couple of templates, and it gets a whole lot worse. The plethora of tools is a good thing; what's needed now is some way to combine them more quickly. (The ideal fix would be some sort of souped-up version of the Mastertools idea, but I don't think it's actually feasible to implement such a tool in a form I'd like to use, especially if you want to make money with it.)
The other key problem is the randomness of high-level combats. Too often, it seems that these battles are determined by who's defense against the save-or-die attack fails first. Cunning strategy and tactics has little place - it's all down to attacking with your most potent attacks in sequence, and hoping your luck holds out longer than theirs. This problem probably can't be solved in the current edition. However, I think a two-step solution might be in order. Firstly, go through the various effects, and assign power levels accordingly. So, blindness might be a CR1 effect, paralysis CR3, and so on (this comes from Monte Cook's site). Secondly, perhaps defences need to be moved from an all-or-nothing defence to a more gradual response. So, a high-level power might have one effect if the save is 30+, another at 25+, a third at 20+, and so on. That way, your high-level Enchanter facing a high-level Fighter doesn't have to sweat while the Fighter rolls his save for the Dominate Person effect, knowing that a 12 means the Fighter is out of action, while a 13 means that the Enchanter is toast. By the same token, the player faced with a really high save DC isn't left with the knowledge that he must roll at 19, or the character he's carefully built up for 8 months is dead.
In closing, I don't think the volume of criticism is really an indication of dislike for a system. On the contrary, it may well indicate the opposite. When faced with a flawed but otherwise good object of art, criticism will be levelled to help the artist improve. When faced with something that's just bad, people will generally write it off, and not give it any more thought. Or maybe I'm just wrong about that.