No, the Papal Magisterium is not always infallible. The idea that the Pope can never err when he exercises the Magisterium is a heresy because it is directly contradicts the dogma of Papal Infallibility, defined by the First Vatican Council. According to Vatican I, the Pope teaches infallibly only when all of the criteria for infallibility are met. Anyone who claims that the Pope is able to teach infallibly under a different set of criteria (greater or lesser), is rejecting this dogma of Vatican I (chapter 4, n. 9).
“So then, should anyone, which God forbid, have the temerity to reject this definition of ours: let him be anathema.”
If anyone claims that the Pope teaches infallibly whenever he teaches, or whenever he exercises the Magisterium, even when his teaching has not met all of the criteria taught by Vatican I, such a person is a heretic, who is denying the infallible teaching of Vatican I, and who is automatically excommunicated.
See the longer explanation in my article:
Is it a Heresy to Believe that the Ordinary Magisterium is Infallible?
Vatican II also taught that this same set of criteria must be met for a teaching of the Pope to be infallible. (Lumen Gentium, n. 25).
Now all infallible teachings, regardless of whether they were taught under Papal Infallibility, or by an Ecumenical Council, or under the Universal Magisterium, require the full assent of faith, also called divine and catholic faith.
“Therefore, by divine and catholic faith all those things are to be believed which are contained in the word of God as found in Scripture and Tradition, and which are proposed by the Church as matters to be believed as divinely revealed, whether by her solemn judgment or in her ordinary and universal magisterium.” (Vatican I, chapter 3, n. 8.)
The solemn judgment of the Church is exercised in Papal Infallibility and in the definitions of Ecumenical Council. But the ordinary and Universal Magisterium also teaches infallibly, and these teachings also require the full assent of faith (divine and Catholic faith).
“This Magisterium is not above the divine word but serves it with a specific charisma veritatis certum, which includes the charism of infallibility, present not only in the solemn definitions of the Roman Pontiff and of Ecumenical Councils, but also in the universal ordinary Magisterium, which can truly be considered as the usual expression of the Church’s infallibility…. With respect to the non-infallible expressions of the authentic magisterium of the Church, these should be received with religious submission of mind and will.” (Pope John Paul II, Address to U.S. Bishops).
So whenever the teaching of the Pope does not meet the criteria for Papal Infallibility taught by Vatican I (and reiterated by Vatican II), his teaching is non-infallible, and does not require the full assent of faith, but only the religious submission of will and intellect.
“This religious submission of mind and will must be shown in a special way to the authentic magisterium of the Roman Pontiff, even when he is not speaking ex cathedra; that is, it must be shown in such a way that his supreme magisterium is acknowledged with reverence, the judgments made by him are sincerely adhered to, according to his manifest mind and will. His mind and will in the matter may be known either from the character of the documents, from his frequent repetition of the same doctrine, or from his manner of speaking.” (Lumen Gentium, n. 25).
Thus, the claim that all teachings of the Papal Magisterium are infallible contradicts the teaching of Vatican I and Vatican II.
May God save the Church from the innumerable heretics currently plaguing His children.