I chose "Install Updates & Restart". It rebooted, and by-and-by I hit ESC to view some progress messages. I saw the update hit 5%, then 10%; and then suddenly a ton of messages scrolled by and it unceremoniously rebooted again. It invited me to log in. Which I did.

A little Gnome bottom-of-the-screen message said, "Software update failed". I hit a button called Details. The details were "Failed to Update: Network access was required but not available."

I thought that a major feature of "offline update" was that it would download the RPMs in advance? So, what is it trying to do with my network? Where is the log of the unsuccessful update?