My original question never pertained to the Novus Ordo per se (I really was thinking of indult, FSSP, neoSSPX sacraments offered by priests with doubtful ordinations). But I also found this which I found helpful...other recent posts had raised similar issues...hopefully others find this helpful too. God bless.
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If intention is necessary for the validity of the sacraments, how can we ever be sure that the sacraments we receive are valid?There can be no doubt as to the necessity of the correct intention for the valid reception of the sacraments. This is explicitly declared by the Catechism of the Council of Trent, when it states that the ministers of the Sacraments:
...validly perform and confer the Sacraments, provided they make use of the matter and form always observed in the Catholic Church according to the institution of Christ, and provided they intend to do what the Church does in their administration (p. 155).
The Baltimore Catechism explains what the expression "intending to do what the Church does" really means, namely:
the intention of doing what Christ intended when He instituted the Sacrament and what the Church intends when it administers the Sacrament.
As a consequence, it follows that if a priest has a positive intention against what the Church does, namely of specifically not intending what Christ intends and what the Church intends, then one of the three elements necessary for the validity of the Mass is absent, and the Mass is invalid.
This is effectively stated by Pope Alexander VIII when he condemned the contrary proposition as Jansenist, namely that baptism is valid when administered by a minister who resolves within his heart not to intend what the Church does (Dz, 1318).
Since none of us can read the innermost intentions of a minister’s heart how, then, does any one of us know whether or not the sacraments we have received were valid. In effect, Saint Robert Bellarmine points out that we can never have a certitude of Faith concerning the reception of a true sacrament, since no-one can see the intention of another. However, in truth we can never have such a certitude concerning human events. The greatest certitude that we can have is a moral certitude, which is also the certitude that we can have about any contingent, singular reality.
However, it is perfectly possible to have a moral certitude. In the traditional rites of the sacraments and of Mass the guarantee of this moral certitude is contained in the rites themselves. For the traditional rites for Mass and the sacraments express the intentions of the Church in a very explicit manner, leaving no room for doubt whatsoever. The same is not the case for the new rites, framed explicitly to be ambiguous, and to be just as compatible with a Protestant intention as with a Catholic one. Since they do not express the intention of doing what the Church does, the intention of the priest cannot be explicitly known. Consequently there is always a doubt as to the intention of the priest in the celebration of the New Mass and sacraments, which does not in any way exist in the traditional rite. The only way to have moral certitude of valid sacraments is to assist at the traditional rite of Mass. Although theoretically it would be possible for a priest to celebrate sacrilegiously in the traditional rite by having a positive counter intention, it is hardly likely, given that the correct intention is repeated several times, which is not the case in the new rite. To the contrary, it is very likely that a Novus Ordo priest celebrate invalidly through lack of intention, since the full and correct intention is not included in the texts of the New Mass.
Note that the Faith is not required for an adequate intention, and that heretics can confer the sacraments validly, provided that they have the intention of doing what the Church does, even though they might not know what that is. This was clear from the third century, when Pope St. Stephen I condemned St. Cyprian’s contention that the baptism of the heretical Novatians had to be repeated. [Answered by Fr. Peter R. Scott]”