A gang of professional pickpockets is currently operating around the Palacio Real, and in particular in the entrance way to the Cathedral next door. It might be advisable to print out a copy of this photo if you expect to visit the Cathedral or Palacio Real in December 2008 or early 2009.
They were seen there regularly in late December 2008, and have apparently realised that the local police will not take significant action against them when they are reported (on two separate occasions they were seen back near the entrance to the Cathedral within an hour of a report being made to the local police).
If you see them, you may be interested in watching them discretely for a few minutes to see if they steal a purse. If you manage to get a photo of them stealing a purse, the police might take some action against them.