I had the same issue and I didnt tweak Firebug at all (newly installed). For me it started to get slow after I activated the console and the script tabs and debugged some Javascript code. The page I was debugging was not responding for a few seconds every time I tried to do something and it took ages to switch between tabs in the browser. However, after inactivating the console-tab in Firebug everything went back to normal.

TL;DR
Try inactivating the console tab in Firebug, that seems to be the cause of the problem (at least it was for me).

Hope that helps.

Now I know Firebug is free, and it’s the only tool that does what it does. So I guess we’re kind of stuck here…

Yet another case of newer not being better. Old Versions FTW

First, disable Firebug’s Console, Script, and Net panes. Do this by clicking on the down arrow next to each tab’s name and select “Disabled.” This doesn’t prevent it from collecting data however. Firebug may still be turned on for specific domains, and this is easy to do without realizing it or remembering it later.

To turn off site-specific capabilities, click on the arrow on each of the aforementioned tabs again and select “Sites…” You can now remove specific web sites. Note that you’ll have to repeat this for each of the three panes — Console, Script, and Net — individually.

Last of all, John J Barton recommends setting all options to their default values. These options can be found by entering “about:config” (without the quotes) into Firefox’s address bar, then typing “extensions.firebug” into the filter text box. For any preference whose status is not “default”, right click on it and select “Reset.”