I recently upgraded my Zimbra Open Source Edition from zcs-6.0.5_GA_2213.DEBIAN5.20100131173855 to zcs-7.2.0_GA_2669.DEBIAN5.20120410001957; this is in preparation to migrating to 64-bit version of Zimbra. There were no errors that I noticed during the upgrades.

Here is the upgrade path I followed:
zcs-6.0.5_GA_2213.DEBIAN5.20100131173855 (This version has been running for several years)
zcs-7.2.0_GA_2669.DEBIAN5.20120410001957 (Currently running)

My server is able to receive and distribute email locally just fine, but I can't send email.

Here is the output from the /var/log/zimbra.log file:
Jan 5 16:53:06 mailtmp1 postfix/smtp[10326]: 1528413F83: to=<harlanb2002@gmail.com>, relay=relay.dnsexit.com[]:8001, delay=6.9, delays=0.19/0.08/6.4/0.26, dsn=5.7.1, status=bounced (host relay.dnsexit.com[] said: 550 5.7.1 <harlanb2002@gmail.com>... Relaying denied. Proper authentication required. (in reply to RCPT TO command))
Jan 5 16:53:06 mailtmp1 postfix/cleanup[10202]: 1163313F84: message-id=<20130105225306.1163313F84@mailtmp1.vpn>
Jan 5 16:53:06 mailtmp1 postfix/qmgr[3755]: 1163313F84: from=<>, size=3661, nrcpt=1 (queue active)
Jan 5 16:53:06 mailtmp1 postfix/bounce[10339]: 1528413F83: sender non-delivery notification: 1163313F84
Jan 5 16:53:06 mailtmp1 postfix/qmgr[3755]: 1528413F83: removed
Jan 5 16:53:06 mailtmp1 postfix/lmtp[10340]: 1163313F84: to=<harlan@bloomenterprises.org>, relay=mailtmp1.vpn[]:7025, delay=0.62, delays=0.01/0.03/0.06/0.52, dsn=2.1.5, status=sent (250 2.1.5 Delivery OK)
Jan 5 16:53:06 mailtmp1 postfix/qmgr[3755]: 1163313F84: removed

email showing failure:

This is the mail system at host mailtmp1.vpn.

I'm sorry to have to inform you that your message could not
be delivered to one or more recipients. It's attached below.

For further assistance, please send mail to postmaster.

If you do so, please include this problem report. You can
delete your own text from the attached returned message.

The mail system

<harlanb2002@gmail.com>: host relay.dnsexit.com[] said: 550 5.7.1
<harlanb2002@gmail.com>... Relaying denied. Proper authentication required.
(in reply to RCPT TO command)

I'm able to login to the server via the Zimbra Desktop, web interface and admin web interface, all without any problems.

I followed this URL (Zimbra Mail Server Relay Access Denied & ISP Relay with Authentication | Spirit of Change) to setup my authentication again, which seemed to have been lost during the upgrades. No joy.

Does anyone have any other ideas or suggestions? Please let me know if there is any other information you require!

Thank You for your time and attention!