In view of the latest interviews and talks by pope Francis it is worth looking at what a pope really is there for.
Our Lord gave St. Peter the keys of the kingdom of heaven saying "whatsoever thou shalt bind on earth, it shall be bound also in heaven: and whatsoever thou shalt loose on earth, it shall be loosed also in heaven" (Matt 16:19) the commentary in my version of the DR suggests that this 'loosing' refers to the granting of indulgences. In Luke, our Lord tells Peter "Simon, Simon, behold satan hath desired to have you, that he may sift you as wheat: but I have prayed for thee, that thy faith fail not: and thou being once converted, confirm thy brethren." (Luk 22:31f). In John finally, st. Peter the first pope is told by Christ "Feed my Lambs", "Feed my sheep" (John 21:15-17).
The Power of the keys, the mandate to confirm and strengthen the brethren, the command to feed the flock of Christ. These are fundamental aspects of the primacy of the pope as the visible head of the Church Militant. As head of the Church on earth he has full, immediate and universal jurisdiction. He is the sign and instrument of unity so that whosoever is not in union with the pope is at best a schismatic, cut of from the Church founded by Jesus Christ as the one way to God the Father. On this way to the Father the pope is guide and leader. It is his duty to bring the sheep -the people of God- through this world to the heavenly sheepfold. It is in order to do this that he is the successor of Peter and vicar of Christ, he is given the gift of infallibility in order to preserve unity of faith and morals.
In order to...
All the power, authority, dignity, jurisdiction and priviledges of the pope are conferred upon him so that he can fulfill his task as shepherd of the Church. (cf. CCC 937) As head of the Church Militant it is his task to guide and lead her in her task "to teach, govern, sanctify and save all men." These are the reasons for which Christ founded her in the first place. The papal Powers and priviledges are of a decidedly instrumental nature.
Now,
St. Thomas Aquinas, in speaking of what is evil or bad defines it as "a lack or privation of good" (cf ST 1a q19). If e.g. a car is incapable of getting you from point A to B two things may be at issue
1) the car is not a suitable means of transportation (as e.g. not designed to drive over water)
2) It is a bad car in that it does not fulfill its' purpose.
Apply this to a pope, not just Bergoglio but any pope. If he fails to fulfill the tasks for which the papacy was instituted by Our Lord then he is ipse facto a bad pope. If he brings disunity instead of unity, if he does not feed the sheep with the sacraments and with sound doctrine, if he fails to be a guardian and protector of the faith, if he fails to guide and rule the Church; i.e. guiding her members towards salvation, towards Heaven, if he fails to represent the interests of Jesus Christ whose viceroy he is, then he is a bad pope. Conversly, if he fulfills these tasks he is a good pope.
Regardless of whether he is a good pope or a bad pope he is still, however, the pope, still the vicar of Christ on earth