startover99's post is the exact issue i have just run into with a client. The use of an SSL cert with a internet FQDN causes the WSUS admin console to error out.
I can confirm having the dual bindings in IIS for the WSUS https site has enabled me to connect to the wsus admin console using server.domain.local (need a self signed cert with server.domain.local as subject name bound to https port 8531 with hostname specified)
and
i can also still use the SSL cert wsus.domain.net.au bound to https port 8531 (no hostname specified) for the servers\clients to connect to the WSUS server & get updates.
Many thanks startover99!!!