I've tried checking the registry, I tried:
regsvr32 /u /s SharingAddin.dll
regsvr32 /s SharingAddin.dll
I have also gone so far as to uninstall Outlook, uninstall the ZCO, reinstall Outlook, re-apply all patches and updates, and reinstall the ZCO. That didn't help. I revoked my rights from the calendar and restored them, and that didn't do anything either. The only "hint" I'm getting is in the Zimbra Send/Receive Progress - Synchronizing fails with "Unknown failure".
Any ideas? Other than upgrade to ZCS 6 or 7, which is in our plans, but wasn't going to happen just yet....