I'm noticing a basic misunderstanding about "hermeneutics of continuity" out there among conservative Catholics. Many apparently take the expression to mean that we are supposed to examine everything the Pope teaches and reject aspects of it that differ from what other popes have taught.
So, for example, when Pope John Paul writes in Mulieris Dignitatem that "subjection" in marriage is to be understood as "not one-sided but mutual" (MD 24), we can reject it as inconsistent with what Pius XI wrote in Casti Connubii about the primacy of the husband (CC 26).
But this a mistake, and one that inevitably leads otherwise good Catholics to adopt a bad disposition toward the Pope—one where they set themselves up as judges over him and his teaching ministry.
What "hermeneutics of continuity" really means for faithful Catholics (as I understand it) is at least twofold:
1) That we are to receive papal teaching with a presumption of continuity, i.e., a basic disposition of trust in the charism of his office.
2) That where different interpretations of his teaching are possible, we are to choose the one that best accords with what has always been taught. So, for example, if a given passage in Amoris Laetitia can be read in two ways, one that is essentially continuous with the Tradition and another that breaks with it, we are responsible to assume that the former is the true interpretation. Even more, if a given teachings seems to us to break with Tradition, we are to look for an interpretation that accords with it.
We are also to keep in mind that the mysteries of our Faith are inexhaustible and beyond human comprehension. The Pope's office is guided and protected by the Holy Spirit because it is too much for merely human powers, no matter how theologically sophisticated and erudite. Further, while the fundamental teachings on faith and morals do not change, the Church's understanding of their practical exigences in each day and age does develop and change. And sometimes continuity on the deepest, most essential level involves discontinuities on a more superficial level. (A little boy's growing into a man involves a change from smooth cheeks to bearded cheeks without any rupture in his basic identity as an individual. If hormones are introduced to try to change the boy into a girl and keep the cheeks smooth, we have a rupture.)
So, the faithful Catholic mind is stimulated, not perturbed by apparent inconsistencies in papal teaching. They cause her to search eagerly—in an attitude of faith and and hope and love—for the deep continuity, which, as Pope Francis likes to point out, not infrequently comes as a surprise.