1) Did you install a valid SSL cert? Outlook will refuse to connect if your using the default self-signed cert. This is an Outlook requirement and there is no way around it.
2) Certain GAL syncs don't complete, there is at least one know issue for that.
http://bugzilla.zimbra.com/show_bug.cgi?id=5741
It will be fixed this week.
Which version of the connector are you using?