Overheard by a friend: “I like Pope Francis. He goes to confession and doesn’t believe in this Papal Infallibility BS. I bet Pope Benedict never went to confession.”
As any cursory Google search will tell you, papal infallibility was dogmatically defined at Vatican I (c.1870) and is only applicable in instances when the pope defines a teaching, moral or theological, that is to be held by the entire church. This is not an everyday occurance, but is most clearly seen in instances when the pope speaks ex cathedra (in his teaching capacity as the Bishop of Rome and successor of Peter) to define already-held Catholic beliefs. Two examples are the declarations of the Marian dogmas of the Immaculate Conception and the Assumption of Mary. Theologians disagree over other instances, but many major scholars would argue that papal infallibility has never been formally exercised aside from those two.
So, papal infallibility has nothing to do with: the sins of a pope, whether or not he would participate in the sacrament of reconciliation, or whether or not the pope can ever be mistaken or say something that is incorrect. The pope is not immune from sin, nor is he unerring: he is human, and we are none of us perfect.