I just installed Zimbra on Ubuntu 6.06 LTS and it's up and running. I can send mail out, however, I'm having trouble receiving mail both from external sources and from account to account on the same box.
Looking in the mail queues under server monitoring on the admin console, I'm seeing all three test messages are listed as "deferred" with the reason "connection refused." However, Zimbra/Postfix does appear to be running as I can telnet to port 25 on the box from an external source.
I'm using an internal IP address on the box and it's behind an IPCop firewall. Traffic on port 25 is being forwarded by the IPCop box. DNS is set up per the Ubuntu Install sticky thread in the Installation section of the forum, and DNS resolution appears to work fine.
I do not have any iptables rules set up on the local box, and again, I can connect to port 25 via telnet and get a response from Postfix, so I'm not sure what could be refusing the connection.