Of course, it is difficult to objectively detail influences Orthodoxy has had on Roman Catholicism. Very often an individual or a small group of individuals may have contact with Orthodoxy, digest certain things which they discovered, and incorporated them into the life and thought of their communion, generally without the knowledge of the Orthodox. Last May I encountered a Roman Catholic priest from France who operates a school for young adults interested in missionary and evangelistic outreach. He gave me a copy of the school's magazine, which sported photographs of the school's chapel, the interior of which was completely frescoed in Byzantine iconography. Other pictures revealed another small chapel filled with icons, as well as the priest himself in Orthodox vestments celebrating the Eucharist. Odd as all of this might be -- imagine how one would react to find an Orthodox church in which the Sacred Heart statue was prominently displayed! -- it does show that, in many ways great and small, Orthodoxy has had some influence, even if it is only external.
The last point, about the Sacred Heart, indicates, however, that there is still a very long way to go. Why is it that, as an Orthodox Christian, I find this Byzantinised image of the Sacred Heart (found at Clerical Whispers: Prayer To The Sacred Heart) quite shocking, and almost a desecration?
I don't mind if Roman Catholics use Byzantine ikons, but this image strikes me as abuse rather than use. It indicates that the gulf is much wider than we think.
Unity is a lot more than Orthodox and Roman Catholic bishops visiting and being polite to each other. I'm all in favour of them doing that, and even doing the same thing with Anglican and Zionist bishops, but it doesn't mean that reunion is imminent.
Some think that it is only a few minor theological issues that can be sorted out quickly. But it’s not just papal primacy and the Filioque that keep us apart, but a millennium of history. We differ in soteriology (Anselm’s theory of the atonement, which swept the west, never got much traction in Orthodoxy), ecclesiology (the Orthodox temple versus the Roman monolith and the Protestant heap of stones) and missiology (Roman missiologists believe that Orthodox missiology is derived from Origen).
All these have led to a different culture and ethos, and this is just as much theology as the kind of theology that is written in books. And so before there can be any reunion, these things must be faced and examined.
So if Roman Catholics want to have images of the Sacred Heart, I think it would be better if they stuck to ones like the one on the left.
Unlike some writers, I don't think a hasty marriage is imminent. We are far closer to the Oriental Churches, like the Copts and Armenians, than we are to the Roman Catholics, and I don't see reunion happening there very quickly. I'll believe it when I see an agreement that the next Pope of Alexandria to die will not be replaced, but that the other one will simply move in to succeed him and that thereafter there will just be one. But I see no sign of that happening yet.
Some other posts that point to differences that need to be examined and sorted out before we can say that the time is ripe for reunion: