I had this error when retrieving IMAP mail for an external account on the same server (Zimbra 8.0.6 OSE)
system failure: Folder sync failed, system failure: Synchronization of folder '.....' failed, system failure: Append message failed, APPEND failed: Error in response, Invalid text character '\0'
I googled but couldn't find a lot about that error.
What resolved the issue was:
1. Delete the external account
2. Answer yes if asked to delete the associated folder
3. Add the external account.
Apparently it was no error in the external account, since I could add that account to another account without problems. So probably something was wrong in the original account, in the folder structure. In my case it happened with two accounts, both times in a folder that ended in 'Contacts'.
Hope this helps someone.