Although many sects of Christianity consider their own beliefs to be infallible, Catholicism has a formal, bureaucratic process for adding new inerrant teachings to its canon. When the pope speaks "ex cathedra", officially defining a new dogma, it's becomes something that all Catholics are required to profess. (I like to think he has a special "infallible hat" hanging in his wardrobe.) As the church thoughtfully explains, an ex cathedra statement must be true "independent of the fallible arguments upon which a definitive decision may be based, and of the possibly unworthy human motives that in cases of strife may appear to have influenced the result".
Now, admittedly, it's true that the pope doesn't claim to be infallible about everything he says. (I know, what a humble guy, right?) Although he can theoretically decide to issue an ex cathedra proclamation about anything at any time, it's true that the claim of papal infallibility has only been formally invoked on rare occasions. The last time it was used was in 1950, when Pope Pius XII declared that the bodily assumption of Mary into Heaven was an article of dogmatic belief for Catholics.
However, what's less well known is that an official proclamation from the Pope isn't the only way for the Catholic church to issue an infallible teaching. If all bishops throughout the world at any given time agree on a particular belief, then that belief is considered to automatically be infallibly true and dogmatically binding on all Catholics present and future. The church calls this the "ordinary and universal magisterium". Pope John Paul II, for example, explicitly stated that the prohibition on women priests is a permanent and infallible part of Catholic faith because of this doctrine.
The ordinary and universal magisterium is probably also why Pope Paul VI overruled his own handpicked commission when they recommended that the church permit contraception: because even though the pope has never made an ex cathedra statement about birth control, the unanimous agreement of bishops up till that point made it an infallible matter of morals, and therefore, according to the church, impossible for them to ever change their position.
Now, I've got a question: Under the doctrine of the ordinary and universal magisterium, is it an infallible teaching of the Roman Catholic church that priests who rape children should be sheltered and protected from the law?
If I understand the principle, the dissent of even one bishop would render this null and void as a church doctrine. But, as far as I'm aware, this has never happened. As far as I'm aware, no Catholic bishop anywhere has ever informed the police voluntarily when a priest was accused of molestation, as opposed to turning over said priest because his proclivities were already known or as part of a legal settlement in which that disclosure was compelled.
It seems absurd that the Catholic hierarchy should hold as an infallible truth of faith that the church should protect pedophiles. And yet, the church's officials have consistently acted as if this is the case. They've consistently acted as if avoiding the embarrassment of a sex predator being discovered among the clergy is more important than preventing that person from preying upon children in his pastoral care. Whether they've explicitly said so or not, they certainly seem to think that shielding child molesters from the law is an essential part of Catholic morals.