The Pope is not God, the Church is not beholden to conform to his every whim and private act and personal opinions, etc. Even if we assume it is true that the Pope gave bad advice to some individual, etc. then that’s on him on him and that’s it.
Likewise, the Pope is not necessarily the most learned theologian, the most competent canonist, the best pastor, the most holy Catholic, etc., etc. We’ve been spoiled in recent times as we have had Popes who seem to be these things, but it will not necessarily always be so, as history shows. I think with increased 24-7 media scrutiny of every little act of Popes, seeing their mistakes–or hearing mistakes alleged-- will become more and more commonplace.
Because of this it will be more and more important to keep the proper perspective regarding the papacy. We seem more willing and able to do this with our own ordinary bishops and priests, but the Pope is sometimes treated as more than he is. He is the vicar of Christ, but not Christ. There’s no book I know of about the “Immitation of the Pope” like there is about Christ. But we do reverence the Pope as the vicar of Christ and obey the Pope as the vicar of Christ, and receive the teaching of the Pope as the vicar of Christ, according to his mind and will. The whole Church is only bound to his public acts which are directed authoritatively to the whole Church and the charisms of his office, including his exercise of the infallible teaching authority of the Church, only really exist for the good of the whole Church, in aedificationem, et non in destructionem (to use the traditional phrase describing the limits of the Pope’s authority, cf. 2 Cor. 10:8).
Likewise, if not addressing the whole Church, he exercises some act over a particular portion or individual of the Church which includes us (e.g if he made some decision for my diocese alone, etc.) then we are to obey it unless it commands sin, then we obey God rather than man.
He has no authority to change the truths of faith, or to command or encourage sin. It’s not in his job description. If he were to do so, then the guilt would be his own. And God forbid, should a Pope go so far as to defect from the faith, the whole Church will not follow him into his error–we have the promise of Christ to that effect–the flock recognizes the voice of its pastor and will not follow someone other than its head (although large portions may). It is also a doctrine of the faith (the opposite error was definitively condemned by Sixtus IV) that the particular Church of Rome will never fall into error–so even if the Pope individually did, the Roman Church would still remain as a fixed reference point.
I’m not saying Pope Francis has done any of these things or that it is even likely that he would, but since he is a fallen human being like all of us and every Pope before him and every Pope to come, it is conceivable that he could screw up, just like it is conceivable that any person could. But we can’t let the possibility that a fallen human being may fall short of the duties of his office shake our faith in the true head of the Church, Christ, or the Holy Spirit which animates the Church and guides her in all truth. They will never fail.