Interactively change the gdm login screen background

As root:

ln -s /usr/share/applications/gnome-appearance-properties.desktop \
/usr/share/gdm/autostart/LoginWindow/

Logout.
The properties window is shown when gdm restarts.
Here's a new way to do the same thing, but easier:

xhost +local:gdm
sudo -u gdm dbus-launch gnome-appearance-properties
xhost -local:gdm