In terms of mistakes: I always remember Eru's response to Melkor, which I can't quote but ran essentially, You will see that what you meant for ill, I will ultimately turn to good, and all the evil in your plans will be turned for good.
We may look at Results and come to our conclusions as to what would have been Good, Better, and Best; but we do not see the "God's eye view".
While the Valar may not know what is to come, or be able to follow the Streams of Fate to their final end, that doesn't mean that Eru cannot.
Nor (here's my favorite part) if Eru knows the future, does that mean that Eru has "predestined" or fated everything a certain way; what makes free will mysterious, is that it may be predictable if you know the chooser intimately. That doesn't turn free will into fate. My husband knows that I love chocolate and will choose it over (ugh!) peas anytime day or night. But he is not "making" me choose; it is not my "fate" to choose chocolate over (ugh) peas. He simply knows me well enough to know what I will choose. And if Eru is all-knowing, then he knows what choices we will make, without violating our ability to choose.
Perhaps a more realistic example: Will Aragorn choose to lie, or tell the truth? We know him well enough that we know he will choose to tell the truth, because of who he is. But we are not "fating" him to tell the truth. He simply does, and we know that he will, because we know he is consistent. If Eru knows him intimately (as he does) then Eru knows what he will choose, without making him choose it.
I'm not negating the existance of fate under certain (fateful) circumstances, such as "The Streams"; I'm simply saying that in some cases, knowing the future involves fate, and in some cases, knowing the future simply involves Intimacy with those forming the future and making the choices.
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...down to the water to see the elves dance and sing upon the midsummer's eve.
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