The "error" on the content target is known to be caused when the Directory Browsing module is installed. As it turns out (I only actually realized this other day), the Web Role installer selects Directory Browsing by default (in Common HTTP Components), and arguably that's a defect. Directory Browsing should not normally be installed on a web server unless a specific application requires that functionality. Uninstalling the Directory Browsing module from the Web Server role will eliminate this "error".
The "error" on the iuident.cab target is a manifestation of WSUS installed on Windows Server 2012. The Diagnostic Tool checks for this target in the root of the WSUS website, and WSUS v6 (on WS2012) no longer copies that file to that location.
However, what is impacting the functioning of your client appears to be that the Configure Automatic Updates policy setting has been DISABLED somewhere along the way, or a script is being applied that sets the NoAutoUpdate registry value to TRUE. The second line "Options" refers to the fact that the diagnostic tool could not find the presence of an AUOptions registry value. While AUOptions is not strictly required (it will default to '4' using internal WUAgent settings), the first line "Automatic Update: Disabled" is the critical condition.
Windows Update Agent configuration settings
Automatic Update: Disabled
Options: Not found (There is no such key)