Woe to the children of these times [i.e., 20^th century]! It will be difficult to receive the Sacrament of Baptism and also the Sacrament of Confirmation.

(source: The Story of Our Lady of Good Success and Novena)

According to Canon 742 of the 1917 Code of Canon Law, non-solemn baptism "can be administered by anyone, preserving the required matter, form, and intention."

This was only allowed in cases of danger of death, but it shows the minimum required for validity.  The person administering the baptism does not need to be Catholic or Christian.  A pagan or Jєω, for example, could do an emergency baptism. The intention needs to be the intent to do what the Church does, even if the person has an imperfect understanding of Catholic teaching on baptism or anything else.

An Arian would probably perform a valid baptism.  I cannot imagine under what circuмstances a Mormon would intend to perform a Catholic baptism, but it is theoretically possible.  The faith of the person performing the baptism does not affect its validity.

Catholic baptism? Mormons have the correct matter and form in their baptisms. They use water and the proper Trinitarian formula. They're baptisms are nevertheless presumed invalid by the Church because Mormons deny the Trinity, and an Arian baptism would be invalid for exactly the same reasons: the intention is wrong. People who deny the Trinity cannot intend to do what the Church does with the formula "in the name of the Father, Son and Holy Spirit".

In any case, for persosn above the age of reason this is absolutely impossible. TO quote Ott, "The justification of an adult is not possible without Faith (De fide)". As Trent declares of justification, "the instrumental cause is the sacrament of baptism, which is the sacrament of faith, without which (faith) no man was ever justified" But what is this faith? Look at the Athanasian creed please: the Trinity and Incarnation are absolutely essential to it. There is no faith without them.

Yes, I agree that a Mormon baptism is invalid.  I said that if a Mormon intended to do a Catholic baptism, it could be valid.

Consider this statement from Apostolicae Curae ():

The Church does not judge about the mind and intention, in so far as it is something by its nature internal; but in so far as it is manifested externally she is bound to judge concerning it. A person who has correctly and seriously used the requisite matter and form to effect and confer a sacrament is presumed for that very reason to have intended to do (intendisse)what the Church does. On this principle rests the doctrine that a Sacrament is truly conferred by the ministry of one who is a heretic or unbaptized, provided the Catholic rite be employed.

The 2001 docuмent that you cited concerning the lack of validity of Mormon baptism clearly acknowledges that this is an exception.

This explanation becomes even more necessary if one considers that errors of a doctrinal nature have never been considered sufficient to question the validity of the sacrament of Baptism. In fact, already in the middle of the third century Pope Stephen I, opposing the decisions of an African synod in 256 A.D., reaffirmed that the ancient practice of the imposition of hands as a sign of repentance should be maintained, but not the rebaptism of a heretic who enters the Catholic Church. In this way, the name of Christ attains great honour for faith and sanctification because whoever is baptized in the name of Christ, wherever that has taken place, has received the grace of Christ (cf. Denzinger-Hünermann [DH] 110-111). The same principle was upheld by the Synod of Arles in 314 (cf. DH 123). Well known also is the struggle of St Augustine against the Donatists. The Bishop of Hippo affirms that the validity of the sacrament depends neither on the personal sanctity of the minister nor on his belonging to the Church.

The Council of Trent used even stronger wording:
"If any one saith, that the baptism which is even given by heretics in the name of the Father, and of the Son, and of the Holy Ghost, with the intention of doing what the Church doth, is not true baptism; let him be anathema."

Interesting point

Oh yeah? If you like that "interesting point", then consider, for real world, life and death, example in the military, right now, where anyone can validly baptize.

Lotta Mormons there, including snipers (typically two man), ODA/ODD, Humint teams, CAT detachments, etc., etc., etc.

(Bear in mind, we're invoking the Consillier "Church" here as well)

I don't know.  I note that it was in 2005 when the Novus Ordo priest in my parish decided to make up his own words for the Consecration at Mass.

Oh, I'm sure that still happens but I hear fewer and fewer reports of it.  And, actually, the new translation of the Novus Ordo Mass accurately translates the words of consecration so that the NOM might even be valid ... especially when the 1st Canon (=very close to the Tridentine Canon) is used.

Don't think of elephants.

Here is Cardinal Billot's explanation of what "the intention to do what the Church does" means:

THIS ^^^

We have the classic example of people creating scruples about the validity of Archbishop Lefebvre on the grounds that +Lienart was a freemason.  But this correct explanation of intention (from Billot) eliminates all doubt and scruple about nonsense like this.  No one can read the mind of the person conferring the Sacrament, so DOING what the Church does suffices.  Only if the person is insane, pretty much, would a Sacrament be invalid.  So, for instance, the classic case of a senile priest who walks past a bakery and prounounces the words of consecration.  That's NOT what the Church does and would be invalid.

How is it that we can reasonably assume that a Mormon is a heretic at all?