To answer the OP, I have some experience with the argument that the sedevacantists have made in regards to this issue. Before going on, I will preface the following with the proviso that am not nor have been a sedevacantist. In addition, I have no “dog in this fight”.
Firstly, as many Catholics know, 3 things must be present for a sacrament to be valid in the eyes of the Church. Matter, Form and Intent. A basic example would be that if a priest poured water over the head of a Catechumen (or infant), and said “I baptize you in the name of God”, no matter what the priests intentions were, because the correct form was omitted, the baptism would then be invalid. Simply laying hands on the candidate during consecration is not enough. This is key in understanding why some of these groups think the New Rite of Episcopal Consecration are at least “doubtful” or to some, outright invalid.
It’s important to note that in Apostolicae Curae, Sept. 13, 1896, Pope Leo XIII solemnly declared that Anglican Ordinations are invalid by declaring that they were invalid due to defects in the rite:
“… of Our own motion and certain knowledge We pronounce and declare that Ordinations carried out according to the Anglican rite have been and are absolutely null and utterly void.”
Here are the problems which Leo XIII saw with the Anglican Rite, which contributed to its invalidity:
Apostolicae Curae, Sept. 13, 1896: “When anyone has rightly and seriously made use of the due form and the matter requisite for effecting or conferring the sacrament he is considered by that very fact to do 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. On the other hand, if the rite be changed, with the manifest intention of introducing another rite not approved by the Church, and of rejecting what the Church does, and what by the institution of Christ belongs to the nature of the sacrament, then it is clear that not only is the necessary intention wanting to the sacrament, but that the intention is adverse to and destructive of the sacrament.”
He goes on…
“For, to put aside other reasons which show this to be insufficient for the purpose in the Anglican rite, let this argument suffice for all: from them has been deliberately removed whatever sets forth the dignity and office of the priesthood in the Catholic rite. That form consequently cannot be considered apt or sufficient for the sacrament which omits what it ought essentially to signify.”
“So it comes to pass that, as the Sacrament of Orders and the true sacerdotium [sacrificing priesthood] of Christ were utterly eliminated from the Anglican rite, and hence the sacerdotium [priesthood] is in no wise conferred truly and validly in the Episcopal consecration of the same rite, for the like reason, therefore, the Episcopate can in no wise be truly and validly conferred by it; and this the more so because among the first duties of the Episcopate is that of ordaining ministers for the Holy Eucharist and sacrifice.”
“Being fully cognizant of the necessary connection between faith and worship, between ‘the law of believing and the law of praying,’ under a pretext of returning to the primitive form, they corrupted the liturgical order in many ways to suit the errors of the reformers. For this reason in the whole Ordinal not only is there no clear mention of the sacrifice, of consecration, of the sacerdotium [sacrificing priesthood], but, as we have just stated, every trace of these things, which had been in such prayers of the Catholic rite as they had not entirely rejected, was deliberately removed and struck out. In this way the native character – or spirit as it is called – of the Ordinal clearly manifests itself. Hence, if vitiated in its origin it was wholly insufficient to confer Orders, it was impossible that in the course of time it could become sufficient since no change had taken place.”
The argumentation from some is that the form approved by Paul VI did exactly what Leo XIII had cited for the reason that the Anglican orders were invalid.
This is just one aspect of what some view as problematic vs what I cited above from Leo XIII and what Pius XII decreed in Sacramentum Ordinis.
I will post more later…