After upgrading to 13.10, every time I boot I'm shown a login prompt (tty1) for ~30 seconds before lightdm automatically starts.

Everything works fine after that. Any ideas on what I could try to fix/debug this?

My /var/log/lightdm/x-0-greeter.log contains lines like the following:

** (at-spi2-registryd:1381): WARNING **: Failed to register client: GDBus.Error:org.freedesktop.DBus.Error.ServiceUnknown: The name org.gnome.SessionManager was not provided by any .service files
** (at-spi2-registryd:1381): WARNING **: Unable to register client with session manager
WARNING: Failed to open sessions directory: Error opening directory '/usr/share/lightdm/sessions': No such file or directory
** Message: PID 1534 (we are 1534) sent signal 15, shutting down...
** (gnome-settings-daemon:1401): WARNING **: Name taken or bus went away - shutting down

Searching for these errors results in a variety of bugs filed over the years. Maybe a clean install will fix this.