Advantages - You're recognized, you can be demanding and people will just think you're quirky, people want your autograph. Disadvantages - Obsessive stalkers, haters, dating people who just want to be famous and you can't go anywhere without being stopped for an autograph. I'm just guessing, of course. :)
Advantage is recognition and disadvantage is useless publicity.
Advantage lots of money and disadvantage is lots of paparazzi.