The most recent (as of this writing) such post is about Constantinople in 754. Right out of the box the first observation I have is that it is not reckoned an ecumenical council by Catholics, and consequently it may (and certainly did) err. So if there is something "inconvenient" about C-754, it wouldn't be for Catholics. This was an iconoclast council, rejected by Catholics and by Orthodox alike. Secondly, Turretinfan suggests that the snippet he quotes (oddly enough, without any documentation, which is out of character for him) contradicts the doctrine of Transubstantiation. Now such a thing wouldn't particularly surprise me, given that it was an Iconoclast council to start with; what's one more error in the heap? But the peculiar thing is that his quotation includes this, said about the bread:
...this figure of the body of Christ, the bread, is made divine by the descent of the Holy Spirit; it becomes the divine body of Christ by the mediation of the priest who, separating the oblation from that which is common, sanctifies it [emphasis added].So where is the denial of Transubstantiation in this sentence? To the contrary, it's an explicit affirmation of it.
So I don't know what is supposed to be "inconvenient" here. It's an invalid council, rejected by Catholic and Orthodox alike, but which apparently (from the snippet here) nevertheless managed to get something right concerning the Eucharist.
Another such post has to do with the council of Jerusalem in 1672 - apparently an Orthodox one, not a Catholic one. Hence its decisions are not binding upon Catholics, and this isn't particularly relevant to me. But on the whole, and given the historical circumstances with respect to rise of Protestantism at the time, I can't say that I find anything particularly scandalous in it - viewed in its historical context. Uninformed and ill-educated folk ought not to pretend that their ideas about the Bible have any particular authority at all. And in any case such proscriptions are not a question of faith or morals. I can't speak for the Orthodox today, but the CCC affirms the value of reading the Scripture, so long as one understands it in keeping with the teaching of the Church.
A third (and probably the last one for now) such post addresses a single canon (out of at least 64) from the "Quinisext" council (also known as the Council in Trullo) - an Orthodox council of 691. Turretinfan seems to think that canon law ought to be treated as binding forever, and so he appears to think that Orthodox who don't act in accord with it are somehow contradicting the claims of their Church. I don't know for a fact about this, but I would be really really surprised if a canon law like this one (dealing with who may teach and where) is supposed to be treated as valid for all time. That's certainly not how canon law is treated in the Catholic Church. Judging from commenters at his blog, it appears that the Orthodox do not treat canon law as dogmatic, either.
In short: I don't see how these posts represent anything "inconvenient" at all. They don't amount to that for Catholics, and I'd be tremendously surprised if they were for Orthodox, either.
It appears that Turretinfan would do well to familiarize himself with the Catholic teaching on the authority of councils in (for example) CCC §880-892 and Lumen Gentium 25.