There's some interesting stuff going on at The Continuum. There has been some discussion there the past few days of what it would mean for someone claiming to be within the Anglican Communion (of their specifically "continuing" variety) to endorse the CCC in its entirety, which, apparently, some Anglicans claim to do. There is a post discussing the Society of Saint Michael (one of said groups), a post discussing the question whether some Anglican bishops formally signed a copy of the CCC at a public Mass in Rome; and a post rehearsing the contents of the CCC teachings on Papal primacy (880-887). For your added delectations, there is a comment in the discussion section of that first one in which Fr. Robert Hart (a frequent contributor to First Things!) disses yours truly in a delightfully snotty fashion. (But then, I deserved it.)
The question of whether, and if so, to what extent, an Anglican may comfortably subscribe to the teachings of the CCC came up at this blog recently, in my discussion with Tobias Haller (see the comments section of this post). Clearly, Papal primacy is the major sticking point (to quote Hart: "the teaching in the CCC about the papacy is one of only a very few places where Anglicans cannot agree with the content"), but given the way most Roman Catholics understand the nature of Papal Primacy--especially in the developed West--it is not clear that there is really all that much at stake. If one is willing to accept most of what is in the CCC--including, I suppose, such things as the content of the teachings on, say, the Immaculate Conception, the Church's indefectibility, etc., then the teachings about Papal Primacy simply disappear in the mix. If, by contrast, one were to say that one accepted all of the teachings in the CCC except those on Papal Primacy and all other teachings that could reasonably be traced to an inordinate amount of influence on the part of the Papacy, then one would have a uniquely non-Roman point of view; but then one would not, in such a case, be able to say that "the teaching in the CCC about the papacy is one of only a very few places where Anglicans cannot agree with the content".
The long and the short of it is simple: the Papacy, whether or not one regards its influence over the various parts of the Roman communion as overweaning, has not exercised anything like the degree of influence in terms of de fide doctrine that some folks have imagined, if it is possible to agree with most of the CCC except for 880-887. If this is right, then the real dispute is not over Papal Primacy, but about Church polity, and this is something that Roman Catholics themselves are constantly bickering about, and indeed, have done for centuries, even prior to the rather sudden invention of the Anglican communion (as an entity distinct from the Roman communion).