I have learned to yield this respect and honour only to the canonical books of Scripture: of these alone do I most firmly believe that the authors were completely free from error. And if in these writings I am perplexed by anything which appears to me opposed to truth, I do not hesitate to suppose that either the [manuscript] is faulty, or the translator has not caught the meaning of what was said, or I myself have failed to understand it. (Nicene and Post-Nicene Fathers, 1:350)
If you encounter an apparent error or tension in the Bible, check for textual errors or translation difficulties. But be prepared to blame your own (fallen, finite) powers of understanding before blaming the Bible or any other Magisterial document. Remember, the Bible is the foundational Magisterial document, but the saints, the popes, the Fathers and the Doctors are similarly free from error. That's why they are held up for example.
So, it is simply impossible to take a statement from one pope, even the current pope (whoever he may be), and claim that another part of the Magisterium (another pope, a saint, a Father or Doctor) contradicts him. There are no contradictions in the Magisterium. Augustine complains about readers who try to wriggle out from under what the Bible is saying by claiming textual corruption:
When these men are beset by clear testimonies of Scripture, and cannot escape from their grasp, they declare that the passage is spurious. The declaration only shows their aversion to the truth, and their obstinacy in error. Unable to answer these statements of Scripture, they deny their genuineness. (Nicene and Post-Nicene Fathers, 4:178)
Similarly, a lot of traditionalists and liberals both make the same claim about papal statements, or other Magisterial statements, they don't like. They claim, "Oh, Pope XXX is mis-teaching, because his statement doesn't match the statement of Doctor YYY. Thus, it falls upon me to correct the Pope!" So, unable to bear the idea that they may have a wrong understanding of Catholic Faith, an understanding that has to change, a lifestyle that has to change, these people deny the genuineness of papal teaching by claiming it is erroneous.
Yeah, that's not how it works. I don't look for errors in Scripture because I don't judge Scripture. Scripture judges me. In the same way, don't bother looking for errors in papal teaching because I don't judge papal teaching. Papal teaching judges me.
And it isn't just me who cannot make these judgements. Even ecumenical councils cannot make these judgements. Nobody can. Nobody judges the pope. No one has the authority to do so.
Now, the next refuge of the scoundrel is to claim that I am advocating some kind of papal idolatry. Ironically, the same people who cheer on Pope Pius IX's statement “I am the church! I am the tradition!” will immediately deny the principle when anyone points out that this statement applies to every single one of Pius IX's successors.
But the very denial betrays the fact that these same Catholics, whether liberal or trad, don't actually accept the Magisterium. They aren't actually Catholics, they are actually Protestants, differing from Martin Luther only in the specific papal statement they have chosen to deny.
Catholics need pay attention to only three people in the world: their parish priest, their diocesan bishop and the Pope. If there is a question about either of the first two, the teachings of the first two are to be weighed against papal teaching.
No priest, no bishop, no parish, no religious order can be trusted to accurately represent the Faith. Ultimately, we can trust only the saints, the Fathers, the Doctors and the popes. When faced with a doctrinal conundrum, we may not have a saint nearby to ask, we are less likely to have a Doctor on call to consult, and all the Fathers of the Church are dead, so that's done. But we always have the pope. He is the one who tells us how to steer course through current problems, how to apply, into any current situation, the principles given by the saints, the Doctors and the Fathers.
So, in questions of doctrine and dogma, the Pope is always correct. In areas of discipline, his opinion is to be preferred over our own, for we are the children and he is the Holy Father, not the Random Stranger. While he may be wrong on discipline, we start by assuming he is correct, as any child would assume when directed by his father. Augustine had the right of it. Follow his lead.