I’m having a problem with the cartoon plasmoid. I’ve decided that I no longer want it on my desktop, but no matter what I do, I can’t get rid of it. It doesn’t matter whether I click the red cross on the plasmoid surround, or deselect it within the top-right menu. It will disappear at the time, but will have reappeared by the next boot.
What am I doing wrong? 
Works here. You can get back to the default plasmoid setup by logging out, going to virtual terminal (press Ctrl+Alt+F1) loging in with your account (not root) and issuing the following command:
rm .kde4/share/config/plasma-appletrc
Now log out (Ctrl D) and press Ctrl+Alt+F7 to get back to the graphical login screen. Now you should see the default plasmoids on the desktop with KDE4.
By the way some important updates related to KDE4 were released yesterday, see if installing those updates help solve the problem you are facing, before deleting the plasma-appletrc file.