Mancini first appears in the Season 5 premiere. He seems to have a resentment for the team and especially Jane, but not Lisbon. He got into a fight with Cho and Rigsby at the crime scene in The Crimson Ticket. Jane provoked him in front of a federal judge, claiming that he was one of Red John's confederates inside the FBI since he had a red glass bead inside his pocket. (Jane claimed that Lorelei told him that Red John's accomplices have them to identify each other.) Jane planted it but no one saw him touching Mancini. So he freaked out, threw a bottle of water at Jane, and chased him through the whole building.
In Not One Red Cent, one can see that he has a thing for Lisbon when he asks her to join him in a poker game.