With the new release of OS X 10.8, the Gatekeeper will popup the following warning, when you try to start a signed Java applet:

The applet has been signed with a valid code signing certificate and will work correctly on other platforms as well as previous versions of OS X. If I change "Allow applications downloaded from:" to "Anywhere", it works correctly.
As far as I can figure out "The digital signature could not be verified", actually means something like "the signature has not been made with a Mac Developer ID".
So: Can I sign Java applets with a Mac Developer ID? Can I sign it with both a Mac Developer ID and a standard code signing certificate? Is there a better approach?