I've learned the hard way, and I'll bet I have a few more hard lessons waiting. When I create a page, I "stress test" the page for compatibility, and I don't mean just cross browser.
Some of the areas I've found good check out:
1) Color depth -- a biggie. I design in 32 bit color. If I don't do checks at least in 16 bit color, I can get bitten.
2) Font size -- browsers allow users to override the fonts and sizes dictated by the web site. It's worth the time to change browser options and see if the page becomes awful in some way.
4) Window size -- check to see if the page redraws gracefully in different sized windows. How about after a re-size? Netscape can have some very strange quirks when resizing a window. I've seen form input boxes vanish when going to full screen from partial (still don't know a fix for that one, either)
What other areas do people feel are worth considering in designing pages to be broadly compatible?