Sometimes I need to inspect elements that are only showing up on a page if you put mouse over some area. The problem is that if you start moving mouse towards firebug consol
I think you can also do this :
Choose Firebugs Inspect mode
Hover over the item that pops up the element you wish to inspect and then use the Tab key several times to make Firebug active (I found it tricky to see when Firebug was the active component but nothing like trial and error - when I saw that Firefoxes Find Toolbar was active I'd then Shift + Tab backwards twice to get into Firebug.
Then I'd use the L/R arrow keys to contract/expand elements and U/D arrow keys to navigate through Firebugs console
Worked for me anyway!