Let me preface this by saying that I enjoyed Dr. Horrible, I thought it was clever and catchy and funny and moving, and I think it's especially great that they put it up for free.
I've seen a lot of discussion from people who were frustrated by it, though - most by Penny's limited role (specifically, viewing her as a prize two men are competing over, with little agency of her own) and by her fridging at the end. I'd particularly like to address the second point -
other people have already made good arguments as to why they think Penny's character was more nuanced than simply that of "love interest" and why, though the writers could have had her whip out a flamethrower at the end and take control (and that would surely have been satisfying and entertaining), that would make this a completely different story and not the one they happened to be telling here.
First - anyone who thinks a comics geek like Joss isn't aware of
the cliché of 'fridging' female characters is delusional. The twist he and his co-authors have put on it here is, I believe, significant enough to change Penny's death from "cliché" to "poking fun at cliché" - namely, that her death at the hands of the nominal hero (Captain Hammer) is what catapults Dr. Horrible into being a full-fledged super-villain. (A traditional fridging would, of course, go the other way around - the female character's death at the hands of the villain is what forces Our Hero into action.) I think perhaps the problem here is that Dr. Horrible is the character the audience identifies with (in a geek-dominated audience, they probably would side with him anyway, but I think he's quite deliberately set up as a sympathetic character despite his many, many flaws) and so it reads, superficially at least, as the same old-same old: girl's death at the hands of the 'bad guy' (the unsympathetic Captain Hammer) is what drives Our Hero to 'greatness' - admission into the Evil League of Evil.
It's also worth pointing out, I think, that other than the seemingly perfunctory bank robbery with Moist after Penny's death, Dr. Horrible isn't seen to do much that furthers his career. Since Bad Horse had demanded a death, and since Penny's was attributed to him (the reporters ask him why he killed her as he carries her body to the stretcher, and he's blamed for it in the papers) I think the only reasonable assumption is that his admission into the League is the direct result of Captain Hammer pulling the trigger that caused his death ray to explode and inadvertantly killed Penny. It's as if, oh, Superman only got into the JLA because Lex Luthor inadvertently saved Lois Lane's life from a trap that Superman set up to catch Lex, and Supe took the credit for saving her - except, you know, backwards. To me, at least, that reads as irony, but I can see how it might go over other heads.
(I'd also note that, since this is about super-heroes, dead people don't always stay dead. There is talk of a sequel, and the actress who played Penny has said she would return if they make one, so... yeah. Not so much an ending in my books, more of a cliff-hanger.)
I don't think Joss is the feminist demi-god some people make him out to be, but I think his perceived status as such (not self-proclaimed, incidentally - he considers that he's just doing what all TV/movie writers should be doing in the first place) and general popularity lead to his works being picked apart with a fine-toothed feminist comb, and subjected to much harsher criticism than lots of other writers. (And can I also say that I'm kind of sick of hearing "Joss did this, Joss did that"? He's only one of four writers on Dr. H, and I don't think we have any way of knowing which individual came up with which particular line or idea.) It's a 40-minute piece of entertainment put together under difficult conditions (during the writer's strike, using Joss's own money and lots of volunteer labour), not a manifesto of all his (or anyone's) core beliefs. And because a lot of people only watched it once, I suspect a lot of the nuance flew over their heads - it's easy to see this story as following a certain path because we fill in a lot of our own assumptions, stereotypes we're used to (the loser-nice guy who ought to wind up with the girl in the end, the arrogant jerk she's with, etc.) rather than seeing the characters for what they really are.
For instance: much of a geek audience is automatically inclined to sympathise uncritically with Billy, despite the fact that he's basically that creepy guy who puts a woman he barely knows on a pedestal and then goes ballistic when she "rejects" him for a more popular guy. She didn't reject him, because he never asked her; she didn't have a chance to know him, because he would barely talk to her! When she approaches him with the petition, he acts weird and antisocial and way more interested in his evil plan than her - despite the fact that, initially at least, he's designed his evil plan in part to attract her attention and win her affections! It's his remote-controlled van that literally drives her into Hammer's arms, when he 'rescues' her from it - and yet Horrible blames both of them ("what heist were you watching?" "did you notice that he threw you in the garbage?") rather than himself.
The conversation when Billy sporks himself in the leg, though funny, is also, I think, the pivotal turning point in their putative 'relationship' - she's clearly not 100% happy with the way things are going with Hammer, and if Billy had actually said anything to her, he might have had a chance, but he doesn't, and that's where it all starts to go downhill. So, no, he shouldn't have ended up with Penny in the end - he hadn't done anything to deserve that. Yes, she's fed up with Hammer and walks off the stage, but she's not running into Billy's arms either - and I think that speaks volumes about her being a real character and not just a damsel in distress. She doesn't need to whip out a flamethrower to show agency, in my books - strength can be shown in other ways.
Yes, it has messages amid the funny. Unfortunately, I think some of them aren't being heard, or understood, and perhaps they're not pleasing either (/MST3K reference).