That's quite a loaded question.
Put it in simple terms, the OO Church considers herself to be the One Holy Catholic and Apostolic Church (probably this includes the EO Church for some OOs). Our most important disagreement with the Roman Catholic Church is Papalism.
As of now, I haven't seen much OO literature on scholasticism, transubstantiation, and purgatory (some OO's simply learn from EO's and borrow their's, but I highly disapprove of this, since we OO's must find our own identity as well). There is an idea on Original Sin and Immaculate Conception. In OO history, there is not one father that gives us Anselmian or Aquinanian language terms of Original Sin, but there is debate on it within the OO community. The Immaculate Conception is one that depends on the definition of Original Sin. OO theology would hold that humanity is essentially no different before or after the Fall, as Sts. Athanasius, Cyril, and Severus have taught. What is different is the grace of incorruption. However, man is not essentially incorrupt. As I understand it, the "definition of Original Sin" according to Catholic theologians does not question the state of corruptibility in humanity, but rather juridical state of humanity. There is hint that some OO theologians have taught the juridical, but have not stressed it as much.
There are many Coptic bishops who are adamantly against Purgatory and Immaculate Conception.
I have read a letter by St. Severus condemning apokatastasis as far as OO belief of the afterlife is concerned.
Ecclesiology is flexible, I think. We stress nowadays that no bishop is above another, even if it be the archbishop, who is "first among equals", so to speak.
There is an Apostolic succession among the Catholics, but this is questioned insofar as the dogmas of the Catholic Church are questioned. Likewise, the priesthood, the sacraments, and the salvation of Catholics are also questioned in the point of validity, but usually not in the point of where to go in the afterlife (i.e. we try not to judge you all to hell, although in all fairness, some OO's may).
To put it in HH Pope Benedict's words, we consider the Catholic Church "defective," and, unlike what Catholics think of us, in some ways "heretical" as well.