I have seen 'private interpretation' of, say, the Scriptures excoriated and the notion rejected as foreign to the Church...my question is this: without exercising private interpretation...how do Orthodox know just what the Church teaches?
We don't. At least, not on every little iota and tau.

I've talked with you, as you know, about this privately. We tend to build fences around more general truths rather than delineate "official truths" that preclude (are you proud of me, Linus7?) any pesky laypersons who might try to think for themselves! (

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So we don't always know exactly what we can say on *every single subject.* Granted. But we are *very* sure when we come up against something we *can't* say. We know said person's gone outside our fence.
As for contradictory beliefs inside these fenced in areas, well, one is free to hold to either one -- we would recognize that one or both would have to be wrong -- as the Church hasn't proclaimed such.
As for, "Well, fine, but how do you know when a fence is really a fence and when it's just a post or whatnot?" Check the liturgical and prayer life of the Church, for starters; if something wildly contradicts that, it's not good. The prayers of the Church are Her lifeline, her living connection (the "living tradition," if you will) and communion, both with God and those who've gone on before. If anything can be seen to be a "delineation" or definition of doctrine, that'd be it.
A question for you: What issues do you see in which Orthodox Christians blatantly contradict each other in terms of "official teaching," with one on the inside of a fence and another on the outside, with both being considered Orthodox? This, to me, would be the only cause for alarm.