When you hover over a running task on the taskbar, Windows shows a small thumbnail preview of all windows in that application.
Now, what if you could click a pin button any of these preview windows that stopped it from closing. You could keep an eye on another windows progress (moving files/ music/video / games etc) while viewing another application fullscreen. Kind of like PIP.
edit: Maybe this wouldn't work as it would get in the way of hovering over another running application to see it's preview.
So another idea would be that if you click a shortcut on any running task it will display a copy of it's windows thumbnail preview in a predefined location on your monitor.
