The most specific clarity of the authority of the Pope came in the first Vatican Council in 1870. It was there that the infallibility of the Pope was declared. This is not an absolute infallibility (as some--both protestant and Catholic--would have you believe), but rather a specific infallibility in specific situations. In other words, contrary to popular opinion, the Pope's authority was not expanded at Vatican I, but limited. Yes, you read that right. His authority was limited because it said that the Pope is only granted the grace of infallibility when he speaks "ex cathedra" and then gave the limitations on that.
Since the limitations of that infallibility were expressed, the Pope has only spoken "ex cathedra" once; in 1950 when Pope Piux XII declared the Assumption of the Blessed Virgin. When Vatican I explained the Pope's authority to be "supreme immediate and universal" it did not declare it to be "in toto" (i.e. in everything he says or does). To put it a bit bluntly: the Pope can make mistakes, say things that are incorrect, and (yes!) even sin.
He is the head of the Church on earth, so we must listen to him and seek to do what he tells us to do -- but always within the boundaries of what we know to be true. His choice of pizza toppings is not Canon Law; and the casual comments he makes on an airplane interview are not infallible dogma. If it appears that the Pope is commanding us to sin, then we seek to obey as closely as we can what it is that he says, while staying faithful to what the Church has always taught to be good and true. Anything else would be disobedient to God. This is what Bishops are for: to help us know how to be obedient when things are confusing.
The tradition of the Church is that the Pope is not "judged" by anyone (even by a priest with a youtube channel who has a bur under his saddle). A good priest once said, that it is not the position of the Roman Catholic Church that a pope is incapable of leading people astray by false teaching. He may be the supreme authority of Christendom, but that does not make him immune to spouting doctrinal errors in his everyday speech. Surprisingly, this fact appears to be unknown to many who ought to know better.
Currently, Canon Law has no provision for how to deal with a Pope who says or does things that are contrary to the faith (which are obviously not said "ex cathedra" and are therefore not infallible). Some sort of process for properly examining how to respond to doctrinal error that a Pope states as his opinion would be helpful for the faithful to find confidence in the hierarchy of the Church once again. The likelihood of that happening anytime soon seems slim, however.
Some even speculated that the current confusion caused by Francis will lead to the Church being forced (by the Holy Spirit, not by us!) to consider this issue and allow a proper solution to be found. After all, problems of the past are what allowed the Church to find resolutions then, and the same can be true for our day. This does not make it easy to endure, but it does tell us that we may be suffering under this pontificate precisely so that our children can do the work of spreading the Kingdom of God in an area that the Church has never considered before, because it never had to deal with it before.
I doubt that any of the faithful who suffered under the Arian heretics 1600 years ago sat back and thought of the future impact of the work they were doing. What a wonderful experience of grace it would be for us to suffer so that our descendants can have this issue worked out and view it just as settled an issue as the Trinity. Let us think of our place in this time as crucial for future generations. Let us remember that we have a part to play in the development of Christ's Kingdom on earth. We are called to this time, let us persevere with dignity and rejoice in the work of God in our lives.