"Firefox support - available soon!" means you're doing things the hard way
I am disappointed to see that Windows Live is not working right in Firefox.[1] Not because I'm all religious about browser support and all that, although Firefox has been my default browser for quite a while. I'm just as dismayed when I see sites that only support Firefox, Safari, or Lynx and say they're adding IE support soon...
That means you're doing it the hard way. It's a lot easier to build a site with cross browser support from the start than to build the whole site out for one browser and fix it. I've done both plenty of times, and I've always regretted it I fix browser compatibility issues after development. It's much easier to fix the HTML when you've just written it than when you have a working site.
If there's the slightest chance you'll need to support "the other browser" then get your HTML right at the start and spot check it as you go. Don't do it because it's the right thing to do, do it because it will save you a ton of time and frustration.
Disclosure: I've had to correct tons of "browser specific issues" over the years. Heck, I've done it plenty in the past week... However, I make a point of checking that the sites generally render in every browser with over a 10% market share throughout the development stage.
[1] I'm not disappointed that it doesn't support more browsers - there's good reason for that.