For Catholics who object to Vatican II, what are the key issues? From time to time I see references to Roman Catholics who object to (part? all?) of Vatican II.  Most commonly I see ads in my local newspaper for traditional Latin masses, but I understand the objections to be more than vernacular versus Latin worship.  I've also heard (as a Jew) that not all Roman Catholics accept nostra aetate, the Vatican II declaration that Jews have a valid covenant with God and don't need to be sought as converts, but I don't know if the anti-NA folks overlap the Latin-mass folks and what other beliefs they share.  Do certain groups object to the whole thing or just parts of it?

I tried to find an answer on Google and it led me to this page at Catholic Answers (no idea how authoritative that is), which in turn led me to the name "Society of Saint Pius X".  This page on their site lists key concerns of: modernism, religious liberty, ecumenism, collegiality, and liturgical abuses (their wording, not mine), but I can't tell if that's all based on Vatican II or if it's something broader.  I also can't tell if SSPX comprises the Catholics who object to Vatican II or if they are just one such group.  (I don't remember seeing that name in the aforementioned newspaper ads.)  I found this C.SE question about whether SSPX is schismatic, which is helpful but doesn't answer my question, which is about the broader platform, not one specific organization.

So: is there a (denomination? ideology?) that describes objectors to Vatican II, or do such objections come from scattered groups or individuals with no over-riding ideology?  If there is an ideology beyond specific people/groups, does it have a name?  And what specifically do they object to -- everything decided at that council or just certain things?
In simplest form: Vatican II declared some very important things to be true which (in the minds of those who object) are radically incompatible with previous Church tradition. As the website of Sodalitium Pianum, an offshoot of SSPX, states:


  The teaching of Vatican II concerning episcopal collegiality, religious liberty, ecumenism, non-Catholics belonging to the Mystical Body of Christ, non Christian religions and particularly Judaism, relations between the Church and the modern world, is in contradiction to the teaching of the Church, of many popes, and many ecumenical Councils. The reform of the liturgy, especially of the Holy Mass, and of Canon Law, are harmful for souls, favor the Protestant heresies, and declare sometimes licit that which by divine right is in fact illicit. ... The Institute [the Institute of the Mother of Good Counsel, which sponsors Sodalitium Pianum], in front of this unprecedented crisis that involves necessarily all that have approved the conciliar documents and the subsequent reforms, realizes that it cannot accept these new doctrines contrary to faith and morals nor incite the faithful to disobedience towards the legitimate authority in the Church.


The other objection they present, again in simple terms, is that Vatican II was only a 'pastoral' council, defining no dogma [and not convened to condemn heresies or resolve a particular issue], thus lacked the doctrinal weight of past Ecumenical Councils - another reason advanced by those at odds with the post-Conciliar Church to maintain their rift with the Church. The following quotes from a Pope and a  future Pope are presented to bolster their arguments e.g.:


  (1)Paul VI:General audience of Jan 12,1966:"In view of the pastoral
  nature of the Council, it avoided any extraordinary statements of
  dogmas endowed with the note of infallibility, but it still provided
  us teaching with the authority of the ordinary Magisterium, which must
  be accepted with docility...." - cf.  Introduction: Doctrinal
  Authority of Vatican II | EWTN
  Library


and 


  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 superdogma which takes away the importance
  of all the rest. - cf. Cardinal Ratzinger's Remarks Regarding the
  Lefebvre
  Schism.
  The translated text of an address by Joseph Cardinal Ratzinger,
  prefect of the Congregation for the Doctrine of the Faith, given July
  13, 1988, in Santiago, Chile before that nation's bishops.


Since the Church does not change her teaching, traditionalists who hold beliefs of this sort feel they're faced with the choice to reject all of Church tradition as they understand it, or to reject Vatican II.