We have seen similar issues, although I only have one user on Zimbra/NotifyLink/Blackberry with another due to come in a week or so. Just this past week 3 calendar items (all from remote invitations I believe) got added to the user's calendar about 50 times each.
Saw messages in the logs like this...
2009-06-18 14:34:11,466 INFO [btpool0-395] [name=xxxxxxx;mid=12;DeviceId=302d2dd1;DeviceType=N otifySync;class=Calendar;client
id=-142220311245359753480;folder=10;SyncCmd=Sync;] mailop - Adding CalendarItem: id=34307, Message-ID=<xxxxxxx.xxxxxxxxxxxxx
464.JavaMail.root@mail.infocentricity.com>, folderId=10, folderName=Calendar, invite=Happy Hour Logistics.
It appeared to me that it was happening because of an issue on the blackberry device. I upgraded the notifysync software on the blackberry and today things seem to be functioning normally. If anyone else sees this kind of behavior please add details to this thread. I'll try to note NotifySync version numbers if I see similar results over the next week or two.
thx
scott