You can remove the dots, at least you can in Ubuntu 12.04. There is a magic setting in one of the LightDM configuration files.
UPDATE: the I documented used to work, but now in 12.04 Final, it doesn't! Stay tuned to the end for the latest solution...
Scratch this, it died with the 12.04 release candidate!
Now we have to open a terminal and poke a bit of code in there to tweak a settings file that can't be accessed any other way I know yet.
sudo xhost +SI:localuser:lightdm
sudo su lightdm -s /bin/bash gsettings set com.canonical.unity-greeter draw-grid false
Log out to the LightDM greeter; you should see no dots!
Now this is a usability interface imprivement, nobody has explained yet. RC