I often end up with a number of items littering my desktop, and then want
to clean them up.  So I drag them to my "Random Documents" or Trash folder,
or select and Ctrl-X to cut them, and paste them somewhere else.

But this usually doesn't work. Somtimes it just fails.  More often, the
item is moved, but the icon stays there, cluttering my desktop.  When I
move it again, it claims to move again, but it doesn't. 

So it looks like I have two copies. But I don't.  So if I delete the one on
my desktop, I lose both.  Very strange.