Some improvements:

 - Detect username before invent one
 - User creation fails if the user prefix is in uppercase and moodle has usernames in lowercase
 - Hide buttons when auth method is disabled
 - Restrict domains from which accounts can be created
 - Do not show the login button if one of the Google settings (app key or secret) are empty
 - Login Button Images are not shown in login with https
 - Allow users with different auth method enter if the email is the same
 - Change fixed login buttons by get_string calls