There are a couple of ways to get the GUI to be able to run applications as root, sudo passwd root and setting a password is one, changing sudo-mode is another. There is information about both in these forums and I think this information should be in the wiki.
Unfortunately neither of these work with many GUI applications. Neither Leafpad nor the file manager will run as administrator, even after these changes have been made. I have asked about this on several occasions but not had any help.
It's a shame but in many cases there isn't a practical alternative to using a terminal.