There is no list (at least that I’m aware of), but you can get a good idea as a lay person what is and what isn’t using the criteria laid out in “Pastor Aeternus”. What is more, the Catholic Church recognizes three organs on infallibility:
"-the bishops dispersed throughout the world in union with the Holy See;
-ecumenical councils under the headship of the pope; and
-the pope himself separately. [when speaking ex cathedra]"
Source: Toner, Patrick. “Infallibility.” The Catholic Encyclopedia. Vol. 7. New York: Robert Appleton Company, 1910. 15 Jul. 2013
http://www.newadvent.org/cathen/07790a.htm.
So are you saying here that the early Church Councils, such as Nicea, were not infallible as they were not under the headship of the pope?
As I said, one can get a good idea by the criteria laid out by the Ecumenical Council of Vatican I, or if you want to dive in deeper one could consult, Theology manuals, Theologians, etc.
This is not the case, many (if not most) are commonly known (or should be by applying the criteria.) If some Theologians disagree on this or that, so be it. This does not mean that it is of no use (Heaven forbid!) Would you rather have a St. Peter in the Apostolic band whose faith could fail, one one who’s faith could not (St. Luke 22:32) ?
I believe that is because you have drawn the wrong conclusions based on not all of the facts.

If you really want to know more, dive into some good Catholic sources (you could start with the article I cited above. Also, you could read the Vatican I document that defined it, “Pastor Aeternus”, to see the usefulness of Papal Infallibility.)