Paulie called in "sick" the day Vito was shot, and the consensus was that he was in on the attempted hit. In the film, during the wedding scene we see that Paulie apparently works for Clemenza, but later I think Clemenza says something about having asked Fredo whether or not Paulie should be replaced, and Fredo said no. Clearly having Paulie around was a breakdown in security, and I wonder whether anyone got blamed for it. I know Clemenza was dispatched to shoot him, perhaps as a sign of loyalte. Then again when Tessio betrays the family, Hagen tells Mike he always thought the traitor would be Clemenza. Maybe that conclusion was based on the Paulie thing.