Yeah, it definitely reads better than it sounds, to the unintiated it would just sound real dumb and confusing onscreen.
I hear it is being used as the nickname for the appreciation society of a former British Prime minister nowadays anyway.
Do movies use the term 'mafia'? It's funny but I am struggling to think of one that has used it and I have seen plenty of mob movies. If there arn't any that use it, it's probably still a bit of a faux paux to make, or that guy with the big nose who runs the mafia, CauseaNostril, with come and ask for a cameo or some dough if you use their trademark.
About the only Marvel movie I can think of that will use the mobs is a Daredevil reboot, the others are all pretty supered up, and i doubt they will use them in a Spider-man movie.
funnily enough, they might be hesitant to use the term 'mob' due to it's constant use in TDK, so they may well use a term like 'syndicate' like you suggested.