Inspector doesn't remain on top of the view after restarting
At least with OpenSuse. Tested with DEs "XFCE" and "Cinnamon". It remains on top of the main window with 2.0.3 after a restart, but not with 2.1, 2.3.2 and the development version (with this versions it stays behind the main window).
A workaround is to deactivate and activate the inspector again (view->inspector or "F8") for the current session.