Here is a guide that will show you how to remove the white dots from the login screen on Ubuntu 12.04.
To remove the whit dots open a terminal window (press Ctrl+Alt+T) and copy+paste the following lines:
sudo xhost +SI:localuser:lightdm
sudo su lightdm -s /bin/bash
gsettings set com.canonical.unity-greeter draw-grid false
When done close the terminal window and enjoy your dot free login screen.