You can remove the dots from the login screen in 12.04-13.10 using this method.
How do you remove the dots from the new lock screen in Ubuntu 14.04?
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To remove white dots, run the following commands in a Terminal:
sudo xhost +SI:localuser:lightdm sudo su lightdm -s /bin/bash gsettings set com.canonical.unity-greeter draw-grid false;exit
Just adding this answer (sourced from comments) for easier view. This worked for me on 14.04 LTS for lock screen. Thanks to S Prasanth for the answer
gsettings set com.canonical.unity-greeter draw-grid false
To do the same for login screen, one has to become do it as the
lightdm user. Which can be done by the method described by @Fat Mind