Are we not discussing one in this very thread? The meaning of ecumenism and the relationship of the Church to non-Catholics. Of course, the liturgical rites and their changes are sometimes raised to the level of dogmatic difference. Religious liberty versus religious tolerance is topical right now, but I concede that is somewhat related to the ecumenism discussion. Ecclesiology, as defined at Vatican II, was controversial even then (see the later-added explanatory preface).
From my experience, the SSPX believes in an essentially different religion than the "mainstream" Catholic Church. It is my belief, based on my research, that the SSPX "version" is more akin to Catholicism as it was believed and practiced prior to 1969. So, there is a very clear rupture there to be seen. In fact, many prominent people in the Church seem to proclaim that rupture as providential.
At any rate, I'm no expert. I was just sharing what caused me to start looking at Church history to see where the continuity could be found (because I reject the development of doctrine idea, at least as it is exemplified here).
CHOY - I agree with you about the lack of communion. This is particularly true when one is mindful that communion for the Catholic Church is not really a communion of faith, but a communion of attachment to the Pope. This is how so many people who believe wildly different things are still in communion. It is becoming similar to the Anglican Communion (although it is certainly not that bad yet). I note, though, that the liberals in the Catholic Church can apparently believe whatever they want. The only ones called to sign a statement of doctrinal belief are the SSPX. It just doesn't make any sense to me.