This question has come up on several threads. I haven't been able to find a more appropriate thread to post on this, but I noticed this:
On the power and character of the primacy of the Roman Pontiff
1. And so, supported by the clear witness of Holy Scripture, and adhering to the manifest and explicit decrees both of our predecessors the Roman Pontiffs and of general councils, we promulgate anew the definition of the ecumenical Council of Florence , which must be believed by all faithful Christians, namely that the Apostolic See and the Roman Pontiff hold a world-wide primacy, and that the Roman Pontiff is the successor of blessed Peter, the prince of the apostles, true vicar of Christ, head of the whole Church and father and teacher of all Christian people.
To him, in blessed Peter, full power has been given by our lord Jesus Christ to tend, rule and govern the universal Church.
All this is to be found in the acts of the ecumenical councils and the sacred canons.
2. Wherefore we teach and declare that, by divine ordinance, the Roman Church possesses a pre-eminence of ordinary power over every other Church, and that this jurisdictional power of the Roman Pontiff is both episcopal and immediate. Both clergy and faithful, of whatever rite and dignity, both singly and collectively, are bound to submit to this power by the duty of hierarchical subordination and true obedience, and this not only in matters concerning faith and morals, but also in those which regard the discipline and government of the Church throughout the world.
3. In this way, by unity with the Roman Pontiff in communion and in profession of the same faith , the Church of Christ becomes one flock under one Supreme Shepherd .
4. This is the teaching of the Catholic truth, and no one can depart from it without endangering his faith and salvation.
5. This power of the Supreme Pontiff by no means detracts from that ordinary and immediate power of episcopal jurisdiction, by which bishops, who have succeeded to the place of the apostles by appointment of the Holy Spirit, tend and govern individually the particular flocks which have been assigned to them. On the contrary, this power of theirs is asserted, supported and defended by the Supreme and Universal Pastor; for St. Gregory the Great says: "My honor is the honor of the whole Church. My honor is the steadfast strength of my brethren. Then do I receive true honor, when it is denied to none of those to whom honor is due." 
6. Furthermore, it follows from that supreme power which the Roman Pontiff has in governing the whole Church, that he has the right, in the performance of this office of his, to communicate freely with the pastors and flocks of the entire Church, so that they may be taught and guided by him in the way of salvation.
7. And therefore we condemn and reject the opinions of those who hold that this communication of the Supreme Head with pastors and flocks may be lawfully obstructed; or that it should be dependent on the civil power, which leads them to maintain that what is determined by the Apostolic See or by its authority concerning the government of the Church, has no force or effect unless it is confirmed by the agreement of the civil authority.
8. Since the Roman Pontiff, by the divine right of the apostolic primacy, governs the whole Church, we likewise teach and declare that he is the supreme judge of the faithful , and that in all cases which fall under ecclesiastical jurisdiction recourse may be had to his judgment . The sentence of the Apostolic See (than which there is no higher authority) is not subject to revision by anyone, nor may anyone lawfully pass judgment thereupon . And so they stray from the genuine path of truth who maintain that it is lawful to appeal from the judgments of the Roman pontiffs to an ecumenical council as if this were an authority superior to the Roman Pontiff.
9. So, then, if anyone says that the Roman Pontiff has merely an office of supervision and guidance, and not the full and supreme power of jurisdiction over the whole Church, and this not only in matters of faith and morals, but also in those which concern the discipline and government of the Church dispersed throughout the whole world; or that he has only the principal part, but not the absolute fullness, of this supreme power; or that this power of his is not ordinary and immediate both over all and each of the Churches and over all and each of the pastors and faithful: let him be anathema.
The boldface made me think of the case of Pope Adrian V, who has also come up, e.g.:
-Adrian V: Even if your argument were correct (It isn't) your example would still fail. In order to become Pope, one must be invested with the Pallium. There was evidently no pallium in the early centuries:"According to the "Liber Pontificalis", it was first used in the first half of the fourth century."
Are you saying that none of the first 33 "popes" were popes? Then you have bigger problems than first thought.
Are you sedevantist, saying that because the last three popes were not coronated, that they were not popes?
The cardinals swore loyalty to Pope Benedict of the Vatican right after his election. They did not wait until his inaugral mass.
Again,the Ultramontanist claims made for deacons like Hilary, combined with this insistence that the papacy is not an order, pulls the rug under the "lack of episcopal character" as an excuse.
Adrian was not. He is generally listed as a courtesy:
Technically, since Adrian V was never ordained bishop, he never truly became the Bishop of Rome, but traditionally he is counted in the papal succession.http://en.wikipedia.org/wiki/Pope_Adrian_V
Pope Adrian VI is too kind. He was papal enough to annull his predecessor's bull, and the bishops under him accepted that.
On the issue of "constitutional crisis" it is not crisis whatsoever. The means for electing a Pope do not need to be set by a Pope. Indeed, the original basis of the current means was not set by any Pope, but by the Second Council of Lyon.
When a Pope lays down a constitution, like Pope Gregory X did, and another annulls it, as Pope Adrian V did, it's big deal. What you argue would be like insisting that John McCain is the Vice President of the United States, since he got the next highest votes, as we are free to ignore the XII Amendment.
The problem for deposing of Pope Adrian V on saying he wasn't consecrated yet has the problem that Ultramontanists claim many non-bishops, e.g. the deacon Hilary at Ephesus II, exercising those supreme powers of the pontificate. Why couldn't a pontiff-elect, especially, for instance, where a non-bishop such as Pope Adrian V nullified "the sentence of the Apostolic See (than which there is no higher authority) [which] is not subject to revision by anyone, nor may anyone lawfully pass judgment thereupon," i.e. the decree of Pope Gregory X, to which "Both clergy and faithful, of whatever rite and dignity, both singly and collectively, are bound to submit to this power by the duty of hierarchical subordination and true obedience, and this not only in matters concerning faith and morals, but also in those which regard the discipline and government of the Church throughout the world."
And if it is so important to be consecrated bishop to take the pontificate, how can it be claimed it is just an "office" (whatever that means) and not a supra-order of the clergy?
vacant sees, even patriarchal sees, do not present a problem in Orthodoxy, as the Orthodox episcopate operates as an ontological whole, and so can hold any see in trust and preserve its apostolic succession. For a Petrine succession of the pontificate, who holds it in trust?
multiple bishops to one see, though uncanonical, can be corrected by the ontological whole of the Orthodox episcopate by economia. Not even rival bishops in a schism, e.g. SS EP Ignatius and Photios, present a problem. Not so two supreme pontiffs. Hence the necessary invention, alongside the pontificate, of the anti-pope, some of which present problems: "antipope" Dioscoros was validly elected, whereas "Pope" Boniface II was not. Then there is this note:
In the list of popes given in the Holy See's annual directory, Annuario Pontificio, the following note is attached to the name of Pope Leo VIII (963–965):http://en.wikipedia.org/wiki/Antipope#List_of_historical_antipopes
At this point, as again in the mid-eleventh century, we come across elections in which problems of harmonising historical criteria and those of theology and canon law make it impossible to decide clearly which side possessed the legitimacy whose factual existence guarantees the unbroken lawful succession of the successors of Saint Peter. The uncertainty that in some cases results has made it advisable to abandon the assignation of successive numbers in the list of the popes.
This is on top of the problem of how the inferiors elevate their superior, contrary to Heb. 7:7.