So I just solved this issue by installing "ATI binary X.Org driver" from Ubuntu Software Centre (for some reason drivers weren't showing up in the normal System > Administration > Hardware Drivers.
However I no longer have any desktop effects but I don't really care.
Note that even before I installed this driver, disabling desktop effects did not fix the problem.
I guess this means that the problem is something to do with the default radeon driver (I have a radeon x800) and/or some special way in which thunderbird displays.
So I just solved this issue by installing "ATI binary X.Org driver" from Ubuntu Software Centre (for some reason drivers weren't showing up in the normal System > Administration > Hardware Drivers.
However I no longer have any desktop effects but I don't really care.
Note that even before I installed this driver, disabling desktop effects did not fix the problem.
I guess this means that the problem is something to do with the default radeon driver (I have a radeon x800) and/or some special way in which thunderbird displays.