Oh God, the CSS/IE patience comment is true but also for Firefox. I bet that I've spent more than a week's time in the past two years just dealing with these issues on my various sites :( Part of that is a learning curve but the other part is just the various browsers deciding to implement "standards" in unexpected ways (or ignoring them all together).
In building our startup I haven't come across any monumental, super mathematically/computer science involved problems, but it's still been extremely challenging and fun. I'd say the challenge/fun comes more from trying to do all the things you listed at once, instead of any one of them singularly.
If nothing else, CSS and IE will teach you patience.