I had a funny example of annoying celebs tonight. I decided to play as a detective for the first time in a long time, and when he was sent on his first APB, he was looking for a female wearing jeans and a jacket, with the "Dislikes Children" trait. He showed up at a lot with three females wearing jeans and jackets, and one of them was a Proper Celebrity! He tried to strike up the necessary conversations to find the tell-tale trait, but the celeb just kept interrupting everything, jumping around and screaming, and the other two sims kept breaking off conversations to watch her.
Eventually, with time running out in the work day, I directed my sim to just arrest the celebrity. It was purely out of spite, but he did earn fame points for it!