As most Phoronix readers will know who experiment with their Linux graphics drivers, when the X.Org Server fails to start usually the first place to look to clues for the failure is generally the /var/log/Xorg.0.log file. If it was one restart ago, /etc/X11/Xorg.1.log. With the GNOME 3.12 GDM, there aren't text log files being generated but systemd's journal component is handling the system log storage. Now to retrieve the X.Org Server logs, the journalctl command needs to be used for fetching the logs, e.g. journalctl -e /usr/bin/Xorg.
Other tips for reading the Xorg.0.log file on the systemd journal can be found via Peter's blog. The good news in moving to the systemd journal is that more logs are stored from the X.Org Server rather than just the past two processes.