I found some answers from EWTN. I am allowed by the Church to take Holy Communion from the Orthodox, which makes sense since they do have valid sacraments. However, the Orthodox may not be too thrilled about that, and may refuse. Still, it wouldn't hurt to ask.
There's the other matter concerning our Sunday obligation. The Church will only allow us to go to an Orthodox liturgy instead if it is not possible to attend the Catholic liturgy, e.g., requires travelling an unreasonable distance. Why this rule at all? I don't have any references in front of me, but I assume it's a pastoral matter. Beware the Catholic who favors the Orthodox liturgy over the Latin Rite liturgy -- he may soon find himself converting to Orthodoxy. Not an entirely bad thing, since their sacraments and holy orders are valid, and their theology is mostly identical with ours and certainly not heretical. On the other hand, the Church naturally prefers a formal and full communion with the East, prior to lifting such prohibitions.
Can't wait. :-)