I just ran into the same problem. Firebox would only partially load zimbra webmail page in ajax mode, but this was limited to 2 machines in the same subnet as the zimbra server. Another machine in a different subnet worked fine, and all used the latest version of firefox (3.6). Internet Explorer worked fine.
On problem machines, I found that using
http://zimbra.example.com exhibited the problem. However, using
http://zimbra worked fine. This lead me to the zimbra server's (CentOS 5) hosts file.
The solution:
In /etc/hosts, I now have
192.168.2.1 zimbra.example.com
instead of
192.168.2.1 zimbra.example.com zimbra
NOTE: I had to remove the alias from /etc/hosts and restart zimbra service.
This seems suspicious of a bug in zimbra whereby sometimes it serves up the host alias instead of the fqdn. But maybe it's just the way zimbra works...?