I got some "solution". This error the orginal poster had is that the Debian Mozilla Version (it's different from the official mozilla.org builds, so this doesnt happen with official builds) uses some startup script. You can't open Mozilla when you have Thunderbird open, Firebird might work (anyway on my pc this also doesnt work; it starts a new Firebird window instead of Mozilla).
Now to the technical side of this, DONT READ IF YOU ARENT INTERESTED
They modified the startscript of Debian Mozilla, so that it uses the x-remote thingy to send a command to FB/TB/Mozilla/whatever. That causes that the Mozilla startscript sends a command to Thunderbird "open a browserwindow". This of course doesnt work, because Thunderbird isnt a browser *g*.