@Seed,
That's the power of a good story teller, that being
Joss Whedon, to make the viewer care for the antihero/protagonist.
Dr. Horrible does do bad and criminal things but like most human beings, he's not a purely caricatured black and white character. He's far more complex and thusly has traits (personality and analogy wise that make him a sympathetic character to the viewer).
I'm fascinated with the intelligence and cultured nature of another infamous doctor,
Doctor Hannibal Lecter.
If you ever watched a thriller of a heist film, it is likely that you would be rooting for the criminal/aka society's deemed bad guy.