Chris Tessone, a priest of the jurisdiction of which I'm a part, has an excellent post about today's feast, and the issues of church polity it raises. I would just add one thought, about infallibility.
The essence of idolatry is to attribute to a creature attributes that properly belong to God. Only God is infinite -- we as humans are by definition finite in every respect. God is omniscient -- we are not. God is omnipresent -- we are not. God is eternal -- we are not, and only know eternal life through God's gift.
Infallibility belongs in this category. No human being, regardless of the office he or she holds, can ever make any statement that is infallible. Nor can any book or institution claim infallibility or inerrancy. The belief that was promulgated by the Roman Catholic denomination at its first Vatican council, that the bishop of Rome is infallible when speaking ex cathedra, is an attempt to claim for a human being something that properly belongs only to God. Similarly, the teaching of the Southern Baptist Convention and others that the Bible cannot contain error is an attempt to claim for a book something that properly belongs only to God.
The Scriptures are a great gift to us, and through them we come to know God's self-revelation through Jesus Christ, fully God (and therefore genuinely infallible) and fully human, and our great redemption through Christ's death and resurrection. We believe that bishops and other church leaders are given grace to lead the church. But to attribute infallibility to either the Bible or church leaders is to distort their roles and put them in the place of the God to whom both are meant to point.