It's not often that I come across bugs in Firebug\Firefox, as both softwares usually act very solid but I guess a major one was bound to happen at some point.
So it seems that the latest version of Firefox, 220.127.116.11, fails to show the CSS properties and applied styles of anchor tags (<A>) in the Firebug style window. Meaning - if you enter inspect mode and go over an anchor element, you only get the last element you viewed before that; Firefox won't show you the CSS properties of the anchor element you selected, or other elements inside it. Bummer.
Luckily though Firefox has rather fast version cycles, with the next one (18.104.22.168) planned to be released March 25, hopefully with a fix to this annoying bug. Until then you can downgrade to an older version of Firefox like 22.214.171.124 and continue working as usual.