Eva,
Your case is quite easy to resolve. What you need to do locate the registry key 'HKEY_LOCAL_MACHINE\SOFTWARE\Microsoft\MSOLCoExistence' add the local admin account that is part of your FIMSync Admin to the local machine. This will correct this issues for you.
My case actually involves, all objects syncing but not password. We are experiencing Event ID 611 which is a pain. We moved Dirsync from Server 2008 R2 to Server 2012 and still nothing, just Event ID 611 all over again.