Don't remember seeing this anywhere in bugzilla - there's always a first, but let's get you on the latest versions to see if it's still a problem.
Yes of course 5.0.2 supports Zimbra Mobile!
Don't forget to read the release notes.
4.5.11 & 5.0.2 Released!
(You don't have to go via 4.5.11, but if you have any ldap replicas you should do so & follow the note on that as well.)
I can't stress enough the importance of making a backup first:
CLI - zmbackup Network Edition Only - Zimbra :: Wiki
You can use the ZCO 4.5.x connector just fine against a ZCS 5.0.x server. It will work, simply without any of the new 5.0 features. Later the users can upgrade to the latest ZCO per their convenience, no need to upgrade the connectors first and then the server.
Of course do upgrade a few of the connectors so we can see if this problem is reproducible. If so, grab some logs & send them to support:
Outlook Troubleshooting Options - Zimbra :: Wiki