Pastor's role

two different levels of inspiration

You're distinguishing between universal and individual revelation. That's a very appropriate distinction to make in this conversation. However, I do believe that universal inspiration exists outside the biblical canon, and I think you do too. Those who hold that "tradition" is a product of the Holy Spirit inherently hold that it is "inspired" to such a degree that all of church dogma and doctrine should account for the tradition of the church. I would suggest that it exists in other areas as well, outside the tradition of the church throughout history.

were the early church councils mistaken in excluding certain inspired books, the very word of God, from the cannon?

Maybe, maybe not. I'm less concerned with whether a bunch of old dead guys made mistakes and more concerned with whether we are making mistakes today. The principle of "near unanimous consent," as I often call it, is a powerful test that affirms a lot of what all those old dead guys said. It doesn't mean they created an exhaustive list of whole inspired texts; only that virtually everyone can agree that, at a bare minimum, those 66 that they selected were/are inspired.

I'd wager there are countless other wholly inspired books out there as well, but it isn't particularly necessary that they all be included in the canon. Perhaps they have duplicitous information, or their substance, while inspired, would have re-shaped the focus of Christianity if they had been included, thereby derailing God's intended path for the church. Or it could be that many texts are partially inspired - that is, that God inspired someone to write something very important, but the person then mixed in God's inspiration with their own thoughts on another page.

did those councils get some of the books in the bible wrong?

This is where the "near unanimous consent" principle comes into play. If someone wants to conclude that one of the 66 books is not inspired, then he must also argue that God is generally hands-off when it comes to guiding his people. Many people do, in fact, argue this exact point, most notably those who subscribe to strict Reformed theology. Of course, that same camp actively professes the office of the papacy to be the anti-Christ, so that's not much of a surprise (and no, I'm not a Calvinist ... or Arminian, for that matter).

Did they ...? If so, how do you know?

The test Jesus gave: "By their fruit you will recognize them." I see the fruit of the 66 books in my own life and in the lives of countless others - and I don't mean merely the "good works" that they prompt, but the type of fruit Jesus references in his parables: when the Gospel springs up in someone, bearing new seed that falls into nearby ground. That is, what disciples are made because of these other texts? Or are there any texts that are bearing bad fruit? That are actively turning people away from Christ?

Now, I know this can seem quite circular: I'm applying a standard in Matthew 7 to prove that Matthew 7 is inspired. First, any conversation about the faith must involve just that: faith. To put our faith in the councils of men seems off to me. To put our "faith" in logic and philosophy also seems off, which is what most of "tradition" appears to be to me. Instead our faith should be in God himself, which can break the cycle of cyclical reasoning. But more specifically, the cyclical reasoning argument only really applies if the Holy Spirit only existed as an active presence on the earth when Matthew 7 was written. But because the Spirit exists in us today and is active in the world today, we have a present reason for trusting in the Scriptures that doesn't involve putting our faith in an ancient council.

Further, were the early councils mistaken in distinguishing true Christian belief (matters of christology) from that of Arians or Gnostics?

My point here is that it doesn't matter what the councils said in the first place. From a historical perspective, it's useful to know how the church got here from where it was, so it does matter in that sense. But on specific issues, like early doctrine, christology, biblical canon, and whatnot, when you ask if they were "mistaken" it sounds to me to be no different than asking if John Piper was mistaken in one of his books published today. No doubt, when he writes his books he also has a council of wise leaders in the church who advise him, provide feedback, who help him discern the Scriptures and generate the content. Or imagine any other book that was written by multiple authors. Or perhaps more germane is the example of biblical translations, like the NIV or the ESV, which were the products of large groups of people working together.

The questions you're asking only actually make sense if we assume that those ancient councils actually had some inherent authority to decide the matters that were before them. Take away this assumption and the whole thing really seems quite silly. I'm not saying it's a wrong assumption, of course. I'm merely saying that of the various positions, this seems a very unlikely one to me - and a position that only becomes prominent if someone has a preconceived notion about church tradition, apostolic success, and the like.

To go back to the original question: were they mistaken? Maybe, maybe not. On most things, I'd wager they were spot on. But I'm not so confident in the allegations that they were Spirit-inspired on a universal level that I would say they got everything right, especially when we see the intense conflicts even within those councils over various things, and the ways that some of the conclusions served to gain incredible political advantage to the people in the councils. Mix this with the fact that many of the "traditions" - even as to the sacrements themselves - are practiced in ways that are in direct conflict with the teachings found in Scripture, it creates a clear contrast between Scripture and tradition on many points. But again, that's just from my perspective. I'm sure the Cathodox community has many intelligible ways to defend their version of practicing the sacrements.

maybe I'm not discussing this topic with a Nicean Christian

To be clear, I affirm everything in the Nicene Creed. That said, I do not hold the Nicene Creed as having any special weight or authority. I see it as no different than a John Piper or John McArthur book that succinctly summarizes what is otherwise authoritative through Scripture. The book's summary is not inspired, but to the degree that they are referencing truths found in an inspired text, it is 100% true all the same.

For example, if I said to you, "God wants you to love your neighbor," my exact phrasing there may not be inspired. What is inspired is the biblical text that I'm referencing - and you know that my words are true, even if they hold no divine authority apart from the source from which I reached my conclusion about what God wants you to do. In the same way, the Nicene Creed doesn't have any actual authority in and of itself as an inspired word of God, otherwise it would be called Scripture - but it is all true because of the source material from which it was derived.

To that end, it's not a question of whether or not you're conversing with a Nicean Christian, which one could rationally say I am; rather, it is a question of whether or not you're conversing with someone who believes that tradition is authoritative in itself, which you could rationally conclude I am not.