Has Mountain Lion broken the ability to show Desktop with a gesture, begin dragging an icon, and unshow the Desktop?
Another way to do this is to map "show desktop" to a hot corner (System Preferences > Mission Control > Hot Corners).


Show the desktop using the four-finger gesture or by using the hot
corner
Drag the file from the desktop to the hot corner, which will restore
the windows AND keep the file in hand
Drop the file onto whichever window you like.


This is how I do it, and it doesn't require any finger acrobatics.