Sometimes, coding for the web is like having a co-worker with a body odor problem. Everyone's far too polite to say anything, so you all put up with it and nobody tells the poor smelly soul. Meanwhile, they sense something's wrong but don't know what.
Web browsers are so insanely great at making sense of tag soup, that if you code only for the end-result--a reasonable strategy, adopted by most when starting out--you can get into all sorts of tangles. Misery ensues: you're stuck with days of fiddling in the dark. You know something's up, but it's hard to see what's going wrong.
In that sense, browsers are lousy at one half of Postel's law. They get the "liberal in what you accept" bit right, but they don't help the developer one bit in implementing "be conservative in what you do." Using three or four different validators for HTML, CSS, etc. often helps a lot, but the state of the browser as an integrated development platform leaves something to be desired.
Although its author Joe Hewitt cautions us to remember that Firebug is still an alpha release, I'd still recommend rushing to install it. If you're developing anything for the web browser this year, it's the most important tool you'll find.
While it won't rid you of the problems of cross-browser compatibility, Firebug will speed you in uncovering the smelly bits of your web application.