The guild list does not show up when using Firefox but does populate when using IE. I don't get an error with Firefox; I just get no data. Figured you'd want to know.
I ran into a similar problem, but for me it's not only the guild list. No matter what search I start, character, guild, "live" ticked or not, I get no data at all in Firefox. The search icon keeps spinning forever, but no data shows up. When using IE, everything's fine. Maybe the problem is on my side, misconfigured FF or whatever, but still, I just can't figure out where I might have to look (esp. as it worked until like 1 week ago)...
Try to put your options in browser to default, and most important: enable javascript in browser. If you still have problems, check out if you have some internet-protection-like program, which might try to mess up things.