An ancient issue between Roman Catholic and Eastern Orthodox is the Filoque, an addition to the Nicene creed, made somewhat organically in western Europe. It got widely adopted and eventually defended by the doctrine of double procession, so from a Roman Catholic perspective, one can't say the words signify anything heretical.
But, even as a Roman Catholic one can argue that the words signify disobedience to both council and pope. The council said don't add anything to the creed. It laid out specific things to be done to people who did add things to the creed. Not council only, but a pope too- because a pope promulgated this council as valid, licit, authoritative, and whatever else you want to call it.
So, regardless of doctrine, the Roman Catholic church is disobedient, to, at the very least, for the purposes of this discussion- itself. The appropriate action, if you care at all about unity, is becoming obedient. Notice that I am framing this in terms of authority. We allegedly have power to change issues of authority, but we can't change issues of doctrine. Thus, we must invite the Orthodox to be charitable with us, and interpret our doctrine of double procession as really meaning what they mean, except we were formulating all this stuff in a philosophical milieu based on aristotelian thinking, so obviously, things can get a little stilted.
Anyway, as one might gather, this holds sway over on one because there are very few charitable Christians thinkers who actually want unity. No, most Christian thinkers are arguably not even Christian, they are ideologues who defend their precious thoughts to the death.
Then there are the feelers- the happy people, the ones who have a pretty god who told them just this afternoon that He loves them. They are irrelevant to this conversation because they already say stuffy old arguments like the spat about the filoque just doesn't matter.
But, on the off chance you aren't an ideologue, you can see how the Roman Catholic church could use the principle of authority to make a move toward unity. We can keep our doctrine AND take the filoque out on the principle of actually being obedient to which ever pope it was that promulgated the Council of Nicea. This idea extends across a variety of spheres, and it would be a good idea for the pope to do some unilateral decentralization, less Rome, more traditional authority back in the hands of the real bishop (the ones with actual flocks).
Why shouldn't, for instance, bishops be able to ordain married men? This is not a doctrinal issue, but one of authority, and those churches already in union with the Roman Catholic Church are already chafing under these artificial restrictions now. Why would any Orthodox Bishop, or for that matter any of the patriarchs even bother, especially since they do really have to be charitable when reading Roman Catholic doctrine? One suspects any follower of Jesus would be predisposed to unity, but let us not forget most are first predisposed to be in unity with those already in their own tradition.
But the forces of Schism and doubt need not fear. The ideologue, even as he hosts a great and wonderful symposium on unifying the Church, shall not improve our chance for unity one whit, for he rather shed blood, or damn someone to hell, than sacrifice a single one of his ideas. Oh, certainly, you can take him for all he is worth; like the American soldier, you can depend on him to defend his homeland while you steal everything, including his wife and children, right out of his home. He shall go to his grave grasping nothing but his ideology in his cold dead fingers. He will be like the allegedly Christian women, who claim to follow the god who said to be fruitful and multiply, and yet devote their fertile years to barren pursuits.