I have had these problems, too, currently with the 5.6.3 update (regular version, not Mac App Store), and it also happened with the update before. (Still on El Capitan 10.11.6 with all security updates.)
The updater volume is mounted at /Volumes/<ID>, and I can manually ditto to /Applications easily, then eject the volume, but the updater itself (Sparkle?) always prints that error.
Question: at which temporary location are the downloaded DMGs stored? In the sweetpproduction directory in ~/Library/Caches? (I have removed that directory, to be safe, because there were a couple of Updater .app bundles in there.)