The one i'd like to see would be an episode where the universal translator stops working (TBH i'm amazed Star Trek has never done this episode already....
Well, they kind of did exactly that on Deep Space Nine
. There was the season two episode "Sanctuary", where the entires first act was about the universal translator not being able to decipher the language of the alien of the week. An then there was "Littel Green Men", where the universal translator wasn't working properly either.
The whole scenario you're describing also vaguely sounds like the season one episode "Babel", in that all the characters can't understand each other anymore.