You can definitely not reject the Council and be a faithful Catholic.
At the same time, the Council did not declare any dogma, not once. It was a pastoral council, which is very clearly stated by the Council itself. Disagreeing with anything in the Council is therefore not an act of heresy, unless of course it has been declared dogma by former Councils or Popes.
We are required to “sentire cum ecclesia” (think/feel with the Church), which means we are required to let ourselves be guided also by Vatican 2. We are however not bound to agree with every detail in it. But we are also not allowed to accuse it of heresy, like some traditionalists do.
There are two fine lines here: Some impose the Council as if it were a kind of “super-dogma”. Even debating if some of the texts may possibly contain weaknesses or be problematic, will make some people accuse you of being heretic or worse. They misunderstand the Council just as badly as the sedevacantists do.
The other is the extent of criticism. As I said above, one can’t be a faithful Catholic, and reject the Council. There is no heresy in its documents. Everything in them is perfectly orthodox.
Sometimes, criticism comes from misunderstanding of the texts. Another times, criticism is really against things that came later, but weren’t mandated by the Council (the turning of the altars, many elements of the liturgical reform, naive ecumenic, etc). In that case, they criticize a “virtual council” (to quote pp. emeritus Benedict), which again other people believe in as if it superseded everything that came before.
The correct understanding of the Council is that it is most definitely not infallible, but its texts can also not just be rejected on one’s own whim. They are legitimate, and accusing them of heresy is really equivalent to creating one’s own “Magisterium”.
But again, I find that most who criticize the Council a lot, don’t really criticize the texts, but everything that happened later. Just like I find that most of those who defend everything that happened later, don’t really defend the Council.
I’ve read through all the texts several times back when I studied Theology. I can’t say I disagree with anything in them at all. I see some weaknesses, though, mainly with regards to clarity. If the texts had been less open to interpretation in some places, perhaps we would have had less problems later on.
But then again, many of the changes happened in spite of passages from the Council being very clearly contrary to those changes. So I don’t think the Council can be blamed at all. And even if it could be, we’re not allowed to reject it. It wouldn’t be the first council to temporarily cause chaos.