No, really, to use this word is to invite ridicule.
If you must use it (and at least you'll be livening up a dull Sunday by giving us someone to snigger at) then do remember that the g is silent. As in tagliatelle.
An imbroglio happens when people disagree, not in a straightforward sock-him-on-the-nozzle sort of way but when people aren't quite sure exactly what's wrong, how to solve it, or what anyone wants, but are still determined to make a fuss about it.
Imbroglio used also to mean a confused heap or jumble (which is again very like tagliatelle) but now we tend to use the phrase teenager's bedroom instead.
Image by Nick.
Word Not To Use Today: imbroglio. This word came to English in the 1700s from Italy. Imbrogliare means to confuse or embroil.