I have just upgraded a box from Jessie to Testing, same problem! I would bump the "severity" up from important to serious since it rendereds the box unusable.
In my case the box gets stuck during installation of memcache. Error getting authority: Error initializing authority: Error calling StartServiceByName for org.freedesktop.PolicyKit1: Timeout was reached (g-io-error-quark, 24) Cannot stop/start services: [....] Stopping apache2 (via systemctl): apache2.serviceError getting authority: Error initializing authority: Error calling StartServiceByName for org.freedesktop.PolicyKit1: GDBus.Error:org.freedesktop.DBus.Error.TimedOut: Failed to activate service 'org.freedesktop.PolicyKit1': timed out (g-dbus-error-quark, 20) Kind regards.