The story behind the cape that the Beatles wore when they came to Australia was that in Amsterdam, when they were on the canal trip, waving to all of the fans, John spots a young man wearing a cape. He really likes it, as do the other Beatles and they say something about wanting one of those capes to Mal Evans. Mal chases this young guy down and finds out what he can about the cape. If I remember correctly, the guy gives him the cape and the boys have a set custom made for them. But that part might not be totally correct.
Anyhow....Neil Aspinall talks about this in the Anthology, that they must have been made out of poorly made materials because once they got wet in Sydney, the dye in the cloth ran and when they took them off in the hotel, the Beatles had blue-ish (not Blue Meanie) skin!
However, they obviously really liked the capes because they continued to use that style in the movie and cover for Help!
This past fall, Paul's cape that he wore in Sydney was up for auction. However, Paul's people pulled it from the auction a few days before the auction started. I am not sure if Paul has the cape back in his possession or what happened to it.