While selecting cards with Doomsday, the opponent can see any cards you're choosing from the graveyard, as they have the green selection outline around them. This leaks information, as Doomsday does not reveal the cards selected, and unless you know your opponent's exact decklist, it cannot be determined from the exiled cards whether or not a given card was chosen.

Steps to reproduce:

Player B puts some cards in graveyard
Player B casts Doomsday
Player B selects some cards from their graveyard
Player A observes that they can see a green outline appear around cards as they are chosen