What kind of exhibitionist content can you achieve? Can you walk around naked with high enough stats?
People already mentioned a few things, but you also often get different dialogues/descriptions if you have the trait and do something which is somewhat exhibitionist in nature (the protagonist will sound significantly more enthusiastic).
Sometimes either having the exhibitionist trait or low inhibitions will unlock an option (for example, working as a maid at the inn, and deciding to work without panties when you are cleaning the old man's room or having sex in the alleys with a drunkard during a random encounter).
Also, at times the trait prevents you from refusing, rather than unlocking something (if you have the trait and notice the peephole in the public bathroom, you won't be able to report it, to name one).
I might have to expand this with more unique stuff to do, however. I'll add it to my "to-do" list.