I use Tools->Reports->Characters to determine if any 'interesting' characters exist. I can then step though through the relevant code char-by-char watching the bottom left corner - I prefer not to delete/replace them en-masse.
Sigil has a plugin to help deal with
Shady Characters. Perhaps DiapDealer could package it as a calibre editor plugin, as he has with his Toolbag plugin.
I too couldn't find a way of highlighting 'invisible characters' via colour scheme. Would be nice to have a toggle to show 'invisible characters' as a user configured character/colour, eg
✘.
BR