(This is a sub-post for Step 6 from Tutorial 11: Starting Your Own Blogger Template)
(An updated content is added below.)
Personally, I don't like the stage of testing in other browsers. It's annoying that other browsers might show your blog differently than the blogs you're designing it in. But if you want all to have access to your blog and see it as nicely as you've designed it, then you have to go through this process. As for my blog and my demo blogs, I designed them in Firefox and tested in IE7. I've received comments that people using IE6 have some trouble with the templates, but I didn't test them in IE6, and not about to trouble myself downloading IE6 and debugging the codes. The way I see it, if Firefox and IE7 get it right, then it's IE6 that's got the problem (not my templates) and it's IE6 that has to debug itself. Anyway, isn't that why IE7 is made in the first place?
Personally, I think Firefox is by far above all. If you're not using Firefox, I suggest you download them right now - it's free, fast, not too crowded with useless buttons, lightweight, and just plain great. And if you're using IE6 and don't want to upgrade to IE7 because your computer is not fit enough to take the load, but you know that viewing blogs is prone to bugs - then Firefox should be the way to go. Plus, the download is quick, the upgrading is efficient and fast, and there's a lot more to this - but I'll just let you see them on your own. So, if you want to get rid of IE and use Firefox instead, the download button is on the sidebar...
I don't really have a tip for debugging. You just have to be patient and solve the problems one by one. The way I avoid problems is by writing a stricter code so they won't have a chance to flip flop or get 'loose'. If you want, you can start designing a template starting from any of my own templates. That way, you can maintain the part of the CSS code that's there to avoid any bugs in different browsers. But I can't guarantee they're 100% bug-free!
I have tested all the templates in all browsers using Browsershots.org and labeled the ones compatible with all browsers (including IE6). There are also some templates compatible with IE6, but have their sidebars pushed down the Blog Posts because their content-box width is wider than the sidebar. So, please check if this is the case if you see your sidebar misaligned.