The main doctrinal issues I see are the following:
1) To consider the Conciliar Church’s new religion as the Catholic Church. In theory and in practice; dealing with Rome and if she were actually the Catholic Church. Publicly Bishop Fellay said that the Conciliar Church has the 4 marks of the Church. This is a scandal which leads to be swallowed by wolfs. This error is a mortal sin against charity and prudence. They have the authority but they do not have the faith. In practice you have to deal with them as you deal with the Protestants.
2) To declare publicly, never retracted, that the Novus Ordo Misae promulgated by Paul VI is “legitimate”. Those words mean that this “Mass” obliges in conscience to Catholics since this mass was made a law in a legitimate way. This implies also that the Novus Ordo is for the common good, since whatever is made a law, through that very fact as any law, it is necessarily for the common good. Whereas Arch Lefebvre said it is intrinsically evil. Could be valid, but it is an abomination for God. It cannot be legitimate in any way whatsoever. It is a treason against the faith no to mention that this mass is evil, in a public declaration about the position of the SSPX concerning the Novus Ordo Misae.
3) The SSPX recognizes also the New Code of Canon Law, and it is willing to put itself under it without restrictions. It is an apostasy of the faith, since the new Canon is the setting as a “Rule” of the new religion of Vatican II, which is worse than the Assisi meeting as Arch. Lefebvre said. Just the wish of a “personal prelature” in an automatic manner of putting the SSPX under the new code of Canon Law. This act puts our faith under the obedience of a false religion = apostasy.
4) The SSPX publicly acknowledges that she is ready to pray the “new profession of faith” formulated by Benedict XVI. A master piece of the new religion.
5) The SSPX started few years ago its “aggiornamento” or adapting to the standards of the world, by realizing the scandalous re-branding through a non-catholic organization from Holland, in order to change SSPX’s image so that she would be more acceptable to the world. The SSPX intends to have influence “more and better” towards the world and the Conciliar Church by this re-branding. The SSPX in imitating the strategy of Vatican II: modifying itself so that it will be acceptable to the world.
From these issues flow more errors at the doctrinal level and at the level of prudence and morals.
Another grave thing is that the SSPX cannot any more justify its existence. There is not anymore state of necessity for the SSPX, since their aim has now has changed. The priority is not anymore to defend the faith, it has now another priority: to be united to Rome since she is catholic and the VAT II has many good things. They do not want to continue being “outside” the Conciliar Church. Therefore there is not necessity anymore to be “outside” not obeying the Pope. So this change of direction puts the SSPX in the dilemma of choosing only but one of two possible options: either makes an agreement with Rome or to become schismatic.
Only the priests of the Resistance keep holding the position of Arch Lefebvre and therefore the only ones who can justify the state of necessity, the supply jurisdiction towards the faithful and towards whoever want to continue being catholic.