Actually I do web design on the side, and discovered, much to my chagrin, that it is not so much coding for multiple browsers as it is making sure all of the html tags are properly closed.
I've found IE will "assume" html tags are closed, whereas Netscape and Firefox will not.
Plus, having to put together pages for more than one browser, at least for me, forces me to pay more attention to what I'm putting together. In other words, I can't afford to be sloppy about details.
I found the same problem with Mozilla. I found out that I had to make IE my prime web browser in order to check my webpage before uploading. Mozilla would have my text all over the place. I use Mozilla to surf, just wish I could use it for checking html.
I've been hand coding HTML in Notepad since 1995, and I spend more time trying to get my pages to render properly in every other browser, yet even where neatness is the only thing that counts as far as I am concerned, IE still kicks everyone elses a$$.