One of the problems that is unique in our age is that many pronoucements of the Holy See actually contradict previous Church teachings. So a dilemma is set up: are we to follow Rome's contemporary teachings--or its previous ones? Which have precedence? This problem is not so much apparent in papal encyclicals as it is in statements made by papal organs such as the Pontifical Biblical Commission or by the Vatican Commission for Religious Relations or by the Pontifical Council for Promoting Christian Unity, among others. These have semi-official papal status, but teach doctrines that are out of keeping with Church doctrines affirmed in the past.
The new, post-Conciliar version of the PBC has no actual authority. It can be freely ignored and should be if it contradicts the biblical encyclicals or
Dei Verbum.
I doubt that "many" pronouncements of the Holy See contradict previous teaching, especially when consideration is limited to those documents which actually are part of the Magisterium. Oftentimes, as in the case of religious liberty, the "contradiction" is a result of misunderstanding. For instance, on the SSPX website I saw one article claiming the entire Syllabus Errorum was ex cathedra and that it contradicted Dignitatis Humanae. Of course, both assertions are wrong, but oftentimes this sort of thing is how traditionalists find "contradictions".