I've installed Google Desktop Linux on my Ubuntu 6.06 system and found that Firefox crashes a lot ! And by a lot I mean I couldn't even google for advice ;)
Basically after some log hunting I found out the cause is quite simple: the Google Desktop for Firefox extension is broken.
Just go to Tools->Extensions,right-click Google Desktop Firefox and select Disable.
That seems to be it ! Happy google indexing.
I recommend you also comment on the bug-report here (posted on Ubuntu's Launchpad.net).