I upgraded to WindowFX 3.0. Now, when I use the middle mouse button to tile a window the shadow is left on the desktop. If I go to the task bar and click twice on the app, the shadow is then removed from the desktop.
It appears to me that closing a window to a tile is not actually "minimizing" the window, this explains why clicking on the taskbar icon eventually removes the shadow.
I did not see this behavior before upgrading...