Re: The Joker's background?
I think we do get a little glimpse of something with the bits about his father. Particularly the "You remind me of my father...I hated my father" comes off very sincere. Fathers are definitely a big recurring theme in the trilogy, so the fact that the Joker would hate his father definitely makes sense with the punk, anarchist slant they put on the character. He seemed to really have it in for authority figures, so the idea of it stemming from some major daddy issues seems to have some sense of psychological plausibility.
Now, whether or not the father was actually a violent drunk or just overbearing type with too many rules, etc...hard to say. They keep a lot of him very unknowable, which makes him even more elemental. He's pretty much the Satan of the Batman world. Especially in The Killing Joke and TDK, where he is all about getting people to turn on their beliefs. Tempting people to the dark side, as it were.