There was a thread herein that went on at length about how JP2 spoke infallibly when he issued forth on the inablity of the Church to ordain women. However, there was much discussion within the theological community as to whether or not that was an ex-cathedra statement, and the consensus was that it was not (amatuer theologians lurking in these threads to the contrary).
The only two accepted times a Pope has spoken ex-cathdra has been about the Immacualte Conception and the Assumption, to the best of my knowledge. And on that, I rely on better trained theologians than the lurkers.
As a sub-set of this point, there has been, and continues to be, an ongoing discussion (if you will) concerning the whole issue of authority of the Pope and the bishops, and coupled with that, a discussion of ecclesiology; that is, exactly what is the structure of the Church. There are those who want a very rigid, hierarchical model with the Pope as head, and the bishops reduced to something close to rubber stamp minions. There are others, on the other end of the spectrum, who would reduce the Pope to a figurehead, nice to trot out when there is a special occasion, and pretty sharp looking iin those white robes, but incapable of leading at all, let alone effectively. Vatican 1 dealt more with the Pope; and Vatican 2 dealt more with the bishops. Neither really had the last word to be said on the issues.
Another issue is that most people are not too aware of how the Pope relates to the universal Church (which they usually take to mean the Roman rite). The Eastern rites too often are presumed to be nothing more than people from “over there” who use a lot of incense and have differeent vestments, and us foreign languages. the reality is a bit more complex than that. And while that does not have to do directly with infallibility, it does have to do with when and how the Pope may invoke infallibility.
Note: the above has to do with the Pope exercising the charism of infallibility in an ex-cathedra statement, and not as to his exercise of infallibilty as the head teacher in terms of the Magesterium, or through canonization.