Reading comments on threads such as this one on Thinking Anglicans (which incidentally will also lead you to a wide array of posts/articles on the Covenant) or this one on Fulcrum, or reading an essay such as this one by Father Jim Stockton, I am a little confused as to whether critics of the Covenant wish to see the Anglican Communion united or divided!
One emerging theme is that the Covenant will not unite an already fractured Communion. This is, I think, a fair line of criticism to pursue. It is consistent with a commitment to unity to ask of a proposal, 'Will this, in fact, unite us?' It would, of course, assist people such as myself to learn what the better alternative to the Covenant is! It would also be true, I suggest, that a will to unite combined with the Covenant would see the Covenant working well, whereas a lack of will to unite combined with the Covenant will not see the Covenant working well.
Another emerging theme is that the Covenant is not (really) intended to bring unity but is the outwardly respectable face of a hidden conspiracy to enable the expulsion of TEC from the Communion and thus, by implication, is also an anti-GLBT measure. Thus for various reasons from commitment to GLBT rights to basic Christian compassion to simple respect for local Anglican autonomy, the bluff of the Covenant should be called by rejecting it. I and others dispute this interpretation of the Covenant. But, being this far away, Down Under at the Bottom of the World, there may be a conspiracy at the heart of the Covenant going on which I am unaware of - a remarkable conspiracy because it features ++Rowan at the centre of it, and has even involved the Presiding Bishop of TEC who has been present at key Communion meetings supporting the Covenant.
Personally I prefer to trust the non-conspirational involvement of ++Rowan in the Covenant and to interpret the Covenant as (among other things) a fair call by the Communion for TEC to convince the whole Communion of the theological justification for the moves it has made in recent years. That is, the Covenant is an opportunity for member churches of the Communion to walk together, talk together, and be mutually accountable one to the other ... which, of course, is not only an opportunity for TEC but also for Uganda, Nigeria, Rwanda, my own church, Sydney-within-Australia - all those who have embarked in recent years on courses of action which have raised questions about whether they are Anglican or not - to account for their actions!
But critics of the Covenant do not see the Covenant in this way. Fair enough. But I see the force of their criticism, if prevailing, as leading us further away from unity as a Communion rather than closer to it. The future of the Communion could be bleak because the critics are offering nothing to stop the fracturing.
Essentially criticism of the Covenant boils down to this (as I reflect on the critics): local autonomy of member churches of the Communion is a more important Anglican value than the interdependence of Anglican churches in a Communion. Ultimately this means the Communion will die.