We're running 6.0.4 (network edition) on CentOS 5.3 (RHEL 5.3 with the serial numbers filed off) in test, and we've had some problems with the calendar getting wedged.
One of our Notes users (which Zimbra will replace, once we finish building it) sent a malformed calendar invite to a bunch of users on the test machine, and now CalDAV access is no longer working for *any* users. Further, ActiveSync can't talk to the calendar anymore either, though the web interface and the Zimbra Desktop Client are both functioning correctly.
I'm stumped as to where to look in the logs to try to figure out what's gotten itself wedged. This hit while we were still running 6.0.2, but an upgrade has not fixed the problem. It doesn't appear to matter whether a user received the bad invite or not; I had someone set up Lightning who hadn't received it, and they can't connect to their calendar through iCal or CalDAV either.