Allegedly, Apple is aware of this issue and is looking to release a patch shortly to correct this amongst other issues.
Getting rid of voice memos does not fix it for me because I do not have voice memos. I did a fresh install of Mountain Lion and only downloaded the four albums I have purchased through itunes. Because this is a problem after a fresh install, I think something in iTunes 11 broke it. Are you guys running iTunes 11?
Crazy solution that worked for me: http://www.titanium.free.fr
The app is called Maintenance.
I had so much issues with that for so long. Basically each time I updated iTunes or OS X, my screensaver and Finder wouldn't get the cover anymore. I've run the app called Maintenance, all things are back. I've found other solutions by myself but it feels so dumb having to re-download all the songs or renaming folders. The app took 2/3 minutes, everything was back. Not sure if it's a cache issue somewhere or what but hey, yeah.
Lots of useful ideas on here, but none of them worked for me I'm afraid.
What did work - bizarrely - was downloading the free trial of an App called TuneUp, which is meant to improve the accuracy of your iTunes album covers and song titles. I couldn't see much of an improvement to iTunes having run the App to be honest, but it appears to have fixed the problem with the screensaver, which is now working again after being bust for over a year.