Well, coming from a Catholic background ecumencism generally means praying with infidels, Jews, and other heathens. I do not mind talks between Orthodoxy and the Latins if truth is not compromised. I suppose now I am pretty much convinced of Orthodoxy, though I am still not rushing, but there can be a talk on debatable issues. I think the Immaculate Conception is likely one. I am no longer convinced of it and making it it a doctrine as the Latins have seems to be a problem, but it can make a theory. But that goes back to the Latin versus Eastern west of Original Sin. The Eastern view does not make the conception of the Theotokos being born with Original Sin such a problem, but the post-Augustinian Latin view creates problems. Purgatory some might say can be a theory, but it seems to be too much a denial of the Orthodox idea of death and Hades. Papal infallibility, as I have often said, is the biggest thing between East and West. Yes, with Vatican II Rome has not pushed that anymore, but it is still on their books and their treatment of the SSPX shows that canonically Rome still thinks it is schism to go against the Pope. So in theory the Pope is still Supreme Bishop of all Bishops and Universal in Jurisdiction.
As for the Oriental I do not know too much about them other than they did not agree with the united, single divine-human nature of Christ, rather confusing it. This seems a clear heresy to me, though I know some have said the Orientals do not have the same believes on this as they used to. Like I said I know so little on it, especially since I am just looking into Eastern Orthodoxy myself from a Roman Catholic perspective. Since I was traditional Roman Catholic I am not a fan of kissing Korans or praying with Protestants and Jews, but a union of East and West would be nice, but the issues dividing us seem to be too much. So I am not sure. Vatican II has not helped because now Rome is constantly contradicting its past ways, but not outright. They will not just come out and deny the papal infalibility thing, even if they talk about collegiality after Vatican II.