I run Firefox Nightly 8.0a1 (2011-07-08) on Arch Linux 64-bit with Gnome 3, and I'm having problem with crashes when I try to download files. This doesn't happen in the stable version of Firefox (5) which I also have installed on my computer.
It's possible to open the download manager as long as there are no entries in the download list. But if I start a download of something - the download manager opens with an entry (the current download) and Firefox disappears. It instantaneously vanishes from both the monitor and the process list.
I have tried to remove the downloads.sqlite file from my profile folder, but it didn't help.
I have also tried to rename my whole profile folder to something else, and then created a new, empty profile folder with the name the first one had. When I then started Firefox, it recreated all the default content to the profile folder, so I ended up with a clean, unmodified installation. But it still crashed when I tried to download files. So it doesn't seem to be a problem with the extensions or similar.
Downgrade to an older nightly that works for a week or so, then test again to see if the bug's still there. In the mean time, report the bug on Bugzilla if it hasn't already been. There's really nothing you can do about bugs in nightlies.
(A similar sort of bug that triggered 60 seconds after opening, every time, was what got me out of using nightlies as my main browser.)