Here's one I stumbled into the other day: You can inspect the inspector!
This is in Chrome for Windows (haven't tried Safari or Chrome for Mac).
Hit F12 to open the inspector.
If it is docked, click the undock icon so it's in a separate window.
Make sure the focus is on the separate inspector window (click its titlebar to be sure), and hit F12 again. This opens another inspector window where you can inspect the first one.
This is in Chrome for Windows (haven't tried Safari or Chrome for Mac).
Hit F12 to open the inspector.
If it is docked, click the undock icon so it's in a separate window.
Make sure the focus is on the separate inspector window (click its titlebar to be sure), and hit F12 again. This opens another inspector window where you can inspect the first one.