There's a theory that Paulie was the one who sold Tony out in the finale. I think even David Chase said in an interview "The Walrus is Paul"
There are some clues about this...
-Paulie is supposed to go and meet Butchie along with Carlo but we learned that Carlo has flipped, so Paulie went alone.
-He comes back with a box of scissors. Butchie and/or Albie of NY own a hair salon.
-This might be a bit of a reach as my memory is hazy, but at the sit-down Paulie seems to be patted down rather quickly and just as a formality.
-He refuses Tony at first but then he changes his mind about the position after T tells him Patsy will get it. I think the reason he accepted it was because he knew Tony would get whacked so he didn't want to make Tony suspicious by being uncooperative.

Personally, I don't agree 100% with this, but I think it's plausible. Makes much more sense than the Patsy theory.