I run SysInternal's Process Explorer, but it's often minimized. It's run as administrator. In the preview window, whether I'm showing icons or the other representation (I can't remember what it's called), I see windows/icons for Process Explorer in every desktop, even when it's minimized.
Yes, I know that when the window is unminimized, it will be visible on all desktops. However, this window is minimized. it's not visible ANYWHERE. And yes, it's always been this way, but I haven't mentioned it until now.