When you create a new external content type for security purposes SharePoint 2010 will not assign any permissions. The first thing people try to do is to create an external list using the external data source and try to open it. The following error occurs:
Access denied by Business Data Connectivity.
The first thing I tried to do is check permissions for the current user to the database and check other permissions. Save yourselves some time and jump directly to Central Administration > Application Management > Manage Service Applications > Business Data Connectivity Services. From the drop down context menu on your external data source select Set Permissions. Add users or groups, set actual permissions for each group, keep the propagate option selected.
I am not sure how the permissions are propagated, but I guess there is job that gets executed, so some delay may be expected.
The external list works!