Temporary solution
I got the same problem here. Win-7 ultimate 64bit + ATI Radeon HD 4200.
The problem wasn't there in the beginning, it started after 10 days or so. I don't really remember when the notes first appeared with those white frames. Basically the white frames are supposed to be the shadows of the notes. I think they are like placeholders. Here is a very easy temporary solution. Click the Sticky Notes icon on the task bar to make the notes disappear from the desktop. You may need to click the icon 2 or 3 times to make them disappear. Once they disappear, click the Sticky Notes icon again to make them appear again. And there are the shadows of the notes, and the white frames never appear again... UNTIL you restart the computer.
By the way I recently installed Logitech's setpoint as well. But I don't see how it can cause the problem...