During the last weeks I’ve noticed a strange behaviour of Firebug when working on multiple tabs. Especially if working with several tabs from the same domain (e.g. the front-end and the back-end of a TYPO3 installation), Firebug was annoying. Once opened in the front-end tab, it was automatically also shown in the back-end tab.
I didn’t find any settings regarding this and thus opened a bug report and got a quick answer: It’s by design and can be configured 
Details about it can be found in http://blog.getfirebug.com/2009/07/20/firebug-1-4-activation/ where the activation of firebug is described in detail.
Thanks a lot for the hint, I’ve also found myself being anoyed by this behavior past few days too…