SCCM Task Sequence Error 0x4005(16389)

Scenario

You are deploying Windows 10 x64 1607 update. After you click on the update in software center, it looks like everything is working. Files are getting downloaded and whatnot, but you eventually get the error above - Task Sequence: Upgrade to Windows 10 Enterprise x64 1607 has failed with the error code (0x80004005).

After you click "Close" on that, you look back in the software center and it eventually fails with an error code of 0x4005(16389).  It looks something like this:

WSUS Server 2012 R2: Computers won't show up in console

SCENARIO

You used to use Server 2008 or Server 2008 R2 for your WSUS server.  You are upgrading to Server 2012 R2, but when you point your clients to the new server, they don't show up in the Update Services Console.