Some of the commentators on earlier posts by Fr. Al, and on various posts by Dr. Mike Liccione, who has also addressed this topic at some length (focusing, in his case, on the problem of the natur of the authority by which such teachings are to be accepted or rejected), suggest that the teachings on papal primacy--or more notoriously the doctrine of papal infallibility--are innovations and thus to be rejected as heresy.
I can't pretend to be prepared to say anything so interesting or eloquent as what either Fr. Al or Mike have already said on this topic, but I will add two short remarks of my own. First, I think it is always worth asking about the question of authority, as Mike does. In particular, I'm very interested in the following thought experiment. If I am permitted to reject the teaching of Vatican I because it introduced an "innovation", or because it was "not ecumenical enough", or because its voting was "political in nature", then what is to prevent me from rejecting whatever doctrine I find disagreeable by claiming a similar defect in any Conciliar pronouncement whatsoever? If the answer is supposed to be something like "But come one, we all accept the authority of Chalcedon, indeed the first seven are OK by us--it's only the ones after that which we reject", then it's hard to see how this can avoid begging the question, since whatever criterion one applies to the councils since II Nicea, or IV Constantinople, or I Lateran, or wherever one happens to wish to draw the line, similar objections can be raised going all the way back to Jerusalem. To reject any of them, really, is to establish one's own judgment (or the judgment of others whom one regards, as a matter of one's own judgment, as worth listening to on this issue) as the final arbiter of what counts as a legitimate Council.
My second comment has to do with the very idea of innovation as it appears to be understood in some quarters. The very complex issue of the development of doctrine has been ably handled, I think, by both Fr. Al and Mike in their respective venues, so I won't attempt to address the finial details of that whole theory here. Instead, I will simply point out a principle that was endorsed as long ago as St. Gregory of Nazianzus, a principle that I will call the Principle of Non-ampliative Inference. Fr. Al mentions the Palamite notion of "energies" of God, and this reminds me of a different but possibly related case in St. Gregory--the question of what to call the hupostases of God. In Oration 39 St. Gregory says:
Three individualities or hupostases, if any prefer to call them, or persons (prosôpon), for we will not quarrel about names so long as the syllables amount to the same meaning...The idea here seems fairly clear: to call the individualities "persons" instead of, say, hupostases, is not to introduce a theological innovation, just so long as the meaning of the new term is not different from what everyone already understands to be the object of reference. In other words, the technical term "person" is not ampliative, but rather clarificatory. St. Anselm clearly endores this same principle in his treatise De processione Spiritus Sancti, written, significantly, to a Greek audience in 1103, shortly after the Council of Bari on the question of the Filioque. The upshot of St. Anselm's argument in that treatise is that the of the semantic content of the Filioque clause is not innovative but rather follows by logical necessity from what is agreed to by all parties:
If we should consider the Father and the Son and the Holy Spirit in pairs, it is clear from what I have said that it is necessary either that one of the pair is from the other, since the other is not from that one, or that that one is not from the other, since the other is from that one. For example, if we should pair the Father and the Son, we perceive that the Son is from the Father, since the Father is not from him, and that the Father is not from the Son, since the Son is from the Father. And similarly, if we should consider the Father and the Holy Spirit, we find that the Holy Spirit is from the Father, since the Father is not from him, and that the Father is not from the Holy Spirit, since the Holy Spirit is from him. So also, if we should explore how the Son and the Holy Spirit are related to one another, we shall understand that the Holy Spirit is from the Son, since the Son is not from him, and that the Son is not from the holy Spirit, since the Holy Spirit is from the Son. Therefore, what I said before [in section 1] is evident, that the aforementioned relations, although they are in one thing, cannot let their plurality be absorbed in the unity nor can the unity let its uniqueness be absorbed in the relations.The text here appeals to a distinction, accepted by all the parties at the Council of Bari, between something being Deus and something being Deus de Deo. St. Anselm claims that once you accept this distinction, along with the doctrine (also accepted by all parties) that God is one single thing, with a single substance, the rest follows of logical necessity and cannot rationally be denied.
Theologically the argument deploys a Platonic essentialism that ought to have appealed to the Greeks if for no other reason than its manifest origin in Greek metaphysics but that apparently fell rather flat. The Godhead contains, as a matter of its essence, the asymmetrical relational property pair “from/not from”, and it is this fundamental relational property that defines the relations between the three Persons. Just as the Father begets the Son, the Son is begotten—that is, a non-begetter, establishing the Father as the “from” and the Son as the “not from” elements of the relation when they are brought into comparison. Just as the Holy Spirit proceeds from the Father, the Father is a non-proceeder, establishing the Father again as the “from” element and this time the Holy Spirit as the “not from” element in the relation. Since it is possible for the Son and the Holy Spirit to be considered as a pair, the full essence of the unified Godhead must still be present, otherwise it is not really a unified substance shared by all three Persons. If the “from/not from” asymmetrical relational property is an essential element of that substance, and if that substance is truly a unified singular, then it is necessary that the property will be present in any pairing of Persons, including the pairing of the Son and the Holy Spirit. Since the Son is evidently “not from” the Holy Spirit, we can infer that the Holy Spirit is “from” the Son, and not merely through the Son as by an instrument, per Filium, as the Greeks insisted, but from the Son as source, proceeding from him just as he proceeds from the Father, since the relational property must apply in the same way to every pairing. This point would have been very difficult for the Greeks to accept, and they could not have tried to apply Gregory of Nazianzus’ semantic equivalence rule here even if they had wanted to, since this is manifestly not the same sort of Double Procession that had been advocated by Saint Augustine and provisionally accepted by such Eastern Fathers as Saint Cyril of Alexandria. It was, in fact, in order to nuance the facts about Double Procession that the several Greek technical terms for modes of procession had been developed in the first place, and ex hypothesi those terms did not carry the same meanings as required by Gregory. Taken individually, then, every Person of the Trinity is in fact the same with respect to having the disjuctive property “God who is either from or not from God as origin or source”; taken as pairs, the disjunct collapses into the respective Personal relations, either “God who is from God as origin or source” or “God who is not from God as origin or source”. This is a sameness relation that preserves both unity and distinctness.
Famously, the argument did not exactly carry the day with the Greeks. Their committment to (the non-heretical version of) monarchia constrained them with respect to what they could accept regarding the theological status of the Son as a source of the Holy Spirit. But it seems clear that if they could have been convinced that the Filioque clause did not actually mean something different from what they already believed, they would have been willing to adopt the logical consequences of their own committments.
This is mere speculation, of course, but my intuition is that the Catholic principle of the development of doctrine is not very different from this Principle of non-ampliative Inference. The difficulty lies in getting those for whom it is antecedently attractive to reject those doctrines that they don't like to see this point.