Dogmatically, I think what makes the RC understanding of Mary problematic is the doctrine of Immaculate Conception, which itself is hinged upon the doctrine of Original Guilt. The Theotokos must be spared original guilt so that she can give birth to Christ (who must be sinless, and therefore cannot be guilty of Adam's sin). Orthodoxy rejects the notion of original guilt outright. We are not personally guilty of the sin of Adam.
Further, removing the Theotokos from our fallen nature also removed Christ from our fallen nature. That is, they have a different nature, an unfallen human nature. However, as the Fathers teach us, "That which is not assumed is not saved." How can Christ redeem our fallen nature if he does not assume it?
This means that, in Orthodoxy, the Theotokos is human just like we are human. She is the great example, not the great exception. There is nothing special about her. She's just as human (and only as human) as anyone else. We can all attain to similar glory, having the same starting point as her ourselves.
However, the idea that the Theotokos is a mediatrix or even a co-redemptrix, I think, does exist in Orthodoxy. However, this does not imply some active participation in the Passion of Christ. No, this ultimate and salvific act belongs to Christ alone. However, the Theotokos brings Christ into the world, and so it is through her that He accomplishes His work. As we sing at Sunday Matins,
"since Thou hast given birth to Christ, thou hast delivered Adam from his sin, thou has given joy to Eve instead of sadness through the God-Man who was borne of thee..."
It is through the Theotokos that Christ accomplishes these things, and we honor her for that participation. However, nothing in this implies that she participates especially in Christ's saving passion. Further, since she inherits the same fallen human nature as the rest of us, she is also in need of redemption through her Son, just as we are.