Should forewarn, I've only seen up to the end of season two (the box-set was bought at Christmas for my girlfriend, and we are both very infrequent television-watchers). Just a couple of notes:
The "voice of a generation" pitch in the pilot is delivered during a bad trip and couched in irony, providing creator Lena Dunham with enough cover should the critical viewer wish to interrogate that claim. But I'm mindful to take the boast seriously, since it hits at something true about the profession Dunham (and Hannah) have chosen – the determination to write to a degree requires the belief that you can write something of significance, despite the world doing its level best to discourage such ambitions.
The gaps between Dunham and her character are not as easily distinguishable as she would perhaps like them to be. She puts an awful amount of herself into her creation – including her battle with obsessive compulsive disorder in the second season. I wonder what part wardrobe (or even the lack of it) plays in her personal differentiation technique. Hannah's outfits are often outrageous, hair often unkempt, make-up non-existent, while Dunham looks super suave and composed in interviews. Hannah does (and wears) what Dunham wouldn't dare.
Dunham acknowledged the race problem in the show, and the scenes with Donald Glover in the first two episodes of the second season were an effective, and funny, apology. In fact, the confrontation scene between them was one of the best pieces of writing Dunham has produced. Her (quite valid) explanation for the lack of black actors is that she's half Jewish, half WASP, and wrote what she knew – four characters that represented parts of that culture and heritage. The question to be asked is why other people don't have a HBO series to write about what they know.
Another counter-argument that has been advanced is that someone living in New York would interact with non-white people a lot more than is suggested in Girls. Only having visited the city a few times, I can't judge whether it really is more integrated than what the show presents to the viewer. Either way this shouldn't let Dunham off the hook, not least because Girls is hardly true to life anyway.
In the first episode, the show explicitly sets itself up as an antidote to Sex and the City and the high-flying lifestyle it presents, but is it really a cold injection of realism? While Girls tries to circumvent any attempt to frame it as an aspirational show (featuring uncompromisingly unlikable characters predestined to make the worst of any situation), I think it remains aspirational, since it asks us to care about what happens on screen despite giving us precious little reason to. Marnie in particular displays no redeeming features whatsoever throughout the two seasons, and yet Charlie remains besotted with her (at the end of season two both him and Adam become male incarnations of the manic pixie dream girl). The result of watching all the terrible things these characters keep doing over and over again without lessons being drawn is that their behaviour becomes normalised. You're allowed to be this selfish and callous and irresponsible, because this (the show suggests) is what being in your early 20s is like.
Dunham can save the show from making this conclusion by treating her characters as more than fodder for jokes and drama, and she is capable of it. I say this because episode five of season two, "One Man's Trash", managed to convey a complexity to Hannah that was not evident before. Dunham finally presents us with an explanation for why Hannah is such a self-destructive moron. Hannah courts pain and distress not only to be supplied with material to write about, but because it separates her out from other people and makes her feel special. Unlike normal "selfish" people who want to settle down and be happy, Hannah will beat herself up in order to give expression to the suffering of others. She is the everyman holding the experiences of her generation within her. The fact that this position is itself extremely self-serving and arrogant is a potent irony. Her masochism is what keeps her initial relationship with Adam afloat, and the inklings of an arc suggest itself which will turn Adam into the stable Joshua character Hannah encounters in "One Man's Trash".