There has been a change (one of the dependent modules in Firefox changed its location) and the current Firebug public releases don't work on Nightly.
This problem has been already fixed.
You can watch the following issue to see when fixed version is released (AMO version should be available in couple of weeks) or download test Firebug build (with a patch included) that already works with Nightly
http://code.google.com/p/fbug/issues/detail?id=7208Honza