Jussi Palo wrote a good blogpost about checking Forefront Identity Manager issues…
My problem was that the account didn’t had Replication writes towards Active Directory.
From Technet (http://technet.microsoft.com/en-us/library/ee721049.aspx):
"Active Directory Domain Services (AD DS): At least Replicate Directory Changes permission is needed on the AD DS domain(s) from which you wish to import data for SharePoint Server 2010. This account must be a member of the Farm Administrators group or must be an account that is designated as a User Profile Service administrator. For more information about how to configure Replicate Directory Changes in AD DS, see How to grant the "Replicating Directory Changes" permission for the Microsoft Metadirectory Services ADMA service account (http://go.microsoft.com/fwlink/?LinkId=47854)."