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Currently when you move a window to a specific desktop, either through dropping its taskbar icon on the pager, using a keyboard shortcut, or using right-click -> "to desktop", the window just disappears. There is no real feedback. I think animating this action using compositing would make it seem a lot more natural. The most obvious animation I can think of is the slide animation currently used when switching desktop. However, instead of the whole desktop moving, the window just slides off the screen in the direction of the destination desktop.

Another possible animation would be for the window to "jump" to the other desktop, appearing to rise of the screen and fly through the air towards the other desktop in an arc-shaped trajectory. Other animations, like appear to teleport, fade, or use the magic lantern animation into the pager (if any) would also be plausible.