The pope is "infallible", only when teaching on dogma "ex cathedra",
as I understand it.
However, as stated in my comment,
"the Profession of Faith states that the Catholic must adhere to authentic but non-definitive teaching with ‘religious submission will and intellect." (Cardinal Avery Dulles, SJ, “Magisterium: Teacher and Guardian of the Faith,” (Sapientia Press 2007) (pp. 93, 106).
For CCC 892 states,
Divine assistance is also given to the successors of the apostles, teaching in communion with the successor of Peter, and, in a particular way, to the bishop of Rome, pastor of the whole Church, when, without arriving at an infallible definition and without pronouncing in a "definitive manner," they propose in the exercise of the ordinary Magisterium a teaching that leads to better understanding of Revelation in matters of faith and morals. To this ordinary teaching the faithful "are to adhere to it with religious assent"422 which, though distinct from the assent of faith, is nonetheless an extension of it. — Catechism of the Catholic Church
And while
Donum Veritatis also allows that even if "not habitually mistaken in its prudential judgments," "some Magisterial documents might not be free from all deficiencies," and withholding assent is allowed for a theologian "who might have serious difficulties,"
yet, among other requirements, such a theologian is to,
"refrain from giving untimely public expression to them." - http://www.catholicplanet.com/CMA/heresy-infallibility.htm
According to Pope Pius XII in Humani Generis & Vatican II in Lumen Gentium n.25, even non-infallible teachings are to receive the submission of mind and will of the faithful. While not requiring the assent of faith, they cannot be disputed nor rejected publicly, and the benefit of the doubt must be given to the one possessing the fullness of teaching authority. - Father John Trigilio; http://www.ewtn.com/library/DOCTRINE/TRIGINFL.HTM
Also, While the theologian, like every believer, must follow his conscience, and Joseph Ratzinger (as Archbishop) taught that "over the pope as the expression of the binding claim of ecclesiastical authority there still stands one's own conscience, which must be obeyed before all else,"[2] it cannot be allowed to be determinative of truth, and the Catholic is obliged to form it according to Catholic teaching.[3] cf. http://www.vatican.va/roman_curia/congregations/cfaith/documents/rc_con_cfaith_doc_19900524_theologian-vocation_en.html
Morever, the Catholic Encyclopedia (Infallibility) states,
in the Catholic system internal assent is sometimes demanded, under pain of grievous sin, to doctrinal decisions that do not profess to be infallible...
But before being bound to give such an assent, the believer has a right to be certain that the teaching in question is definitive (since only definitive teaching is infallible); and the means by which the definitive intention, whether of a council or of the pope, may be recognized have been stated above. It need only be added here that not everything in a conciliar or papal pronouncement, in which some doctrine is defined, is to be treated as definitive and infallible.
For example, in the lengthy Bull of Pius IX defining the Immaculate Conception the strictly definitive and infallible portion is comprised in a sentence or two; and the same is true in many cases in regard to conciliar decisions. The merely argumentative and justificatory statements embodied in definitive judgments, however true and authoritative they may be, are not covered by the guarantee of infallibility which attaches to the strictly definitive sentences — unless, indeed, their infallibility has been previously or subsequently established by an independent decision. — http://www.newadvent.org/cathen/07790a.htm
And trying to ascertain which teachings require full assent, and the kind thereof can be exasperating. As a poster on a RC forum dealing with this expressed:
rrr1213: Boy. No disrespect intended…and I mean that honestly…but my head spins trying to comprehend the various classifications of Catholic teaching and the respective degrees of certainty attached thereto. I suspect that the average Catholic doesn’t trouble himself with such questions, but as to those who do (and us poor Protestants who are trying to get a grip on Catholic teaching) it sounds like an almost impossible task.
But the solution (before Francis at least) he was given was just obey everything:
Well, the question pertained to theology. The Catholic faithful don’t need to know any of this stuff to be faithful Catholics, so you are confusing theology with praxis.
Praxis is quite simple for faithful Catholics: give your religious assent of intellect and will to Catholic doctrine, whether it is infallible or not. That’s what our Dogmatic Constitution on the Church demands, that’s what the Code of Canon Laws demand, and that is what the Catechism itself demands. Heb 13:17 teaches us to “obey your leaders and submit to them.” This submission is not contingent upon inerrancy or infallibility. - https://forums.catholic.com/t/catechism-infallible/55096/31
For the alternative can result in what as one poster wryly stated,
The last time the church imposed its judgment in an authoritative manner on "areas of legitimate disagreement," the conservative Catholics became the Sedevacantists and the Society of St. Pius X, the moderate Catholics became the conservatives, the liberal Catholics became the moderates, and the folks who were excommunicated, silenced, refused Catholic burial, etc. became the liberals. The event that brought this shift was Vatican II; conservatives then couldn't handle having to actually obey the church on matters they were uncomfortable with, so they left. ” Nathan, http://www.ratzingerfanclub.com/blog/2005/05/fr-michael-orsi-on-different-levels-of.html