Most notable in the development of these negotiations is the recognition of Vatican II (in principle) by the SSPX. It is a common misconception that the SSPX has historically rejected the entire Second Vatican Council outright. Such is not the case. The problems the SSPX has with Vatican II are similar (if not identical) to problems other traditionalists have had with the Council. These are namely related to the issues of ecumenism and religious liberty of conscience. Most traditionalists have no problem with other areas of the Council, especially Nostra Aetate which further defined and corrected the Church's relationship with Judaism and the Jewish people. When we really pin traditionalists down on their specific problems with Vatican II, we find their major disagreement with the Council is over just a couple things. That being said, traditionalists don't always insist that Vatican II taught heresy, but rather the message conveyed in some of it's documents were vague and convoluted. Further definition was needed, but because it was lacking, Church modernists took the Council's interpretation to extremes, and therein lies the bulk of the problem.
What many mainstream Catholics fail to realize is that traditionalist organizations are reactionary in nature. They are the result of something else in the mainstream Church. In this case, extreme traditionalism is the reaction to modernism run amok. So long as the mainstream Church coddles modernistic interpretations of Vatican II, that go far beyond what the Council actually wrote, there will always be traditionalist organizations charging heresy. The problematic portions of Vatican II must be further defined, to eliminate doctrinal abuse, and it is perfectly within the Holy Father's ability and competence to do so. The following is from an interview on Corriere della Sera, hat tip to Rorate Caeli..
"[Card. Castrillón:] When I delivered the signed decree to Bishop Fellay, we knew nothing of the interview [between Bishop Williamson and the Swedish Television Station], it had been a few days before."
And at that moment?
"[Card. Castrillón:] Evidently, at that moment, the decree was already in the hands of the interested party. I would rather not enter into details, because they go beyond my competence."
"[Card. Castrillón:] Full communion will come. In our discussions, Bishop Fellay recognized the Second Vatican Council, he recognized it theologically. Only a few difficulties remain..."
Maybe on Nostra Aetate, the declaration which represented a turning point in the relationship with the Jews?
"[Card. Castrillón:] No, that is not a problem. It involves discussing aspects such as ecumenism, liberty of conscience..."