1) SSPX seems to teach that Vatican II was not infallible
From their website (link):
Not by reason of the extraordinary magisterium, for it refused to define anything. Pope Paul VI himself, in an audience on January 12, 1966, said that it “had avoided proclaiming in an extraordinary manner dogmas affected by the mark of infallibility” (Cf. the declaration of the Theological Commission of Mar. 6, 1964, and repeated by the Council's General Secretary on Nov. 16, 1964: "In view of conciliar practice and the pastoral purpose of the present Council, this sacred Synod defines matters of faith or morals as binding on the Church only when the Synod itself openly declares so." It never did.).
Nor by reason of the ordinary universal magisterium, because this is not a defining power, but one of passing on what was always believed. The “universality” in question is not just one of place (all bishops) but also of time (always) (cf., Vatican I and PRINCIPLE 6).
Nor even by reason of the simply authentic magisterium, because the object of all magisterium is the deposit of faith to be guarded sacredly and expounded faithfully (Vatican I, Dz 1836), and not to adopt as Catholic doctrine the “best expressed values of two centuries of ‘liberal culture,’” even if they are “purified” (Cardinal Ratzinger, Gesu, Nov. 1984, p. 72. Cf. Gaudium et Spes, §§11, 44).
Before the excommunication was lifted, people scoffed at the idea that the SSPX points had any merit. As far as I know, their re-union with the Roman communion was not conditioned on their denunciation of the points above, and those points are currently (as of 24 January 2009) on their web site.
I found this comment, attributed (here) to Cardinal Ratzinger (now pope):
The Second Vatican Council has not been treated as a part of the entire living Tradition of the Church, but as an end of Tradition, a new start from zero. The truth is that this particular Council defined no dogma at all, and deliberately chose to remain on a modest level, as a merely pastoral council; and yet many treat it as though it had made itself into a sort of super-dogma which takes away the importance of all the rest.
That raises the question: should we be considering those positions stated in the documents of Vatican II to be "the" Roman position, "a" Roman position, or simply the work of private theologians?
It also raises the question of whether Benedict XVI is trying to undermine the changes his former mentor John Paul II put into place. The SSPX viewed JP2 as a neo-modernist, and JP2 excommunicated them. Benedict XVI doesn't seem to be as concerned about SSPX, which makes it appear that he at least partly agrees with their criticism of JP2.
Either way, we have an interesting paradox: there is unity of communion now between SSPX and folks they view as modernist or neo-modernist heretics. There is unity of communion between the most traditionalist of the SSPX bishops and Joseph ("Joe the Vice-President") Biden - one of the highest-ranking pro-murder politicians in the world. There is organizational unity - but there is obvious lack of unity of belief (or practice) on vast number of issues.
Question for Romanist readers: do you think that it is hypothetically possible that JP2 could turn out to be, in the judgment of Rome in 100 years, an anti-pope?