It is well that Article XXI, present in 1571 and 1662, is omitted in the 1801 version (my brackets):
Of the Authority of General Councils. [A] General Councils may not be gathered together without the commandment and will of Princes. [B] And when they be gathered together, (forasmuch as they be an assembly of men, whereof all be not governed with the Spirit and Word of God,) they may err, and sometimes have erred, even in things pertaining unto God. Wherefore things ordained by them as necessary to salvation have neither strength nor authority, unless it may be declared that they be taken out of holy Scripture.
Recall the Jerusalem Declaration's points (4) and (6):
(4)We uphold the Thirty-nine Articles as containing the true doctrine of the Church agreeing
with God’s Word and as authoritative for Anglicans today.
(6) We rejoice in our Anglican sacramental and liturgical heritage as an expression of the gospel, and we uphold the 1662 Book of Common Prayer as a true and authoritative standard of worship and prayer, to be translated and locally adapted for each culture.
If I were a gambling man, I would bet point [A] in Art. XXI will be selectively "read out" of the 1662 BCP and the 39 Articles. But how far will GAFCON engage in selective reading? Should the whole of Art. XXI be omitted? If it were excised, that would seem sufficient to establish the legitimacy of critical reading in confronting formularies: formularies need not simply be taken as authoritative on their face. That is, we would agree excision in principle is permitted, and then we might argue about what is to be cut and what kept. However, the Jerusalem Declaration is silent about any such practice, giving the impression that all will be kept intact--I suspect a thoroughly misleading impression.
On the One Hand
Anyhow, the serious trouble in Art. XXI surfaces in part [B]--it is this bit which leads me to speak of the Articles qua part of the Anglican formularies as rotten. Presumably, the Articles were not found ready-made on golden tablets, and were not dictated by angels; they were produced by an assembly of men. It follows that Article XXI is self-referential in a certain sense. That is, in speaking of assemblies of men, it speaks of the assembly that produced the 39 Articles, and in particular Article XXI. Thus, Article XXI implies that it may be wrong--in effect, that the assembly of men that produced Art. XXI might be wrong about Art. XXI. That is roughly equivalent to admitting that there may in fact be an infallible magesterium or assembly. I am not sure such an admission was intended when the Articles were produced, or is intended now when the Articles are cited as authoritative. Nevertheless, it is logically implied. That is quite a remarkable implication, in my opinion, inasmuch as it had seemed to me at least that the 39 Articles expressed a moderate Calvinist take on the faith. For the admission of the possibility of an infallible magisterium would seem to commit anyone accepting the Articles to a view of ecclesial authority consistent with that of the Roman Catholic Church.
In fact, there is more. As Art. XXI implies the assembly producing the Articles may be mistaken, logically, given Art. XXI, the Articles as a whole may be read so as to be mistaken on all points. It follows, so far as the Articles are concerned, there may be an infallible magisterium, and such a magisterium would not be bound--ceteris paribus--to any point of doctrine expressed elsewhere in the Articles. That would mean strict adherence to the Articles is consistent with--indeed logically requires--accepting the possibility that other interpretations of the faith inconsistent with the Articles are true. That is, the Articles provide a foundation for epistemic humility--but is that the intention of GAFCON in taking them as authoritative? I think not. Of course, if one rejects epistemic humility, it may seem instead that as the Articles stand in the BCP 1662, they are radically self-defeating.
On the Other Hand
Most likely the assembly that produced the Articles did not intend to undermine itself and make a super-subtle endorsement of the Roman See--or of epistemic humility. Far from it.
I take it they simply did not notice the self-reference in XXI and the trouble it causes. Nevertheless, that instance of blindness to scope is not innocent, inasmuch as they probably intended the article to have a wide scope, enveloping assemblies of men in general, and at least those beyond the early ecumenical councils. To try and limit the scope to some assemblies but not others would be troublesome: what criterion could be accepted as plausible and cogent--and yield a non-empty set that excluded what probably were seen as tendentious Roman Catholic assemblies to whose authority the authors of the Articles did not want to be tied?
I do not know, but as a consequence of the incoherence in the Articles, it follows the problem of authority in Anglicanism remained open: i.e. mandating allegiance to an inconsistent set of propositions is not a solution. It probably also may be said in consequence that whatever authority was--and is--exercised in Anglicanism cannot have the Articles as a proper and sufficient foundation. That is, when someone quotes the Articles as an authority carrying some definite content, there is prima facie reason to think that there is a confusion: anything at all follows from a contradiction, e.g. the Law of Duns Scotus: from Q, it follows that if not Q then R--where R can be any proposition at all. Normally, it might be thought that citing Q and not Q--i.e. the Articles--as authority for accepting R--any proposition in contention--is suspect.