The inspector dialog has TBX document scope, i.e. you can open one for each open TB document. Its outcome works on the current selection (of the parent document). By default it opens with the Quickstamp pane selected.
In keeping with Inspector-type windows in other apps the Inspector always sits in front of any other Tinderbox window. The Inspector is invisible when the Tinderbox app loses focus; it does not close but is simply not drawn on screen when another app is in use.
An Inspector's window title will show the name of the parent TB document, a colon, and either the $DisplayName of a single selected or the count number of notes in a multiple selection.