A moment of lucid self-criticism has occurred in the comments here about the relationship between the Pope and the other patriarchs and bishops throughout the Church. There is a dispute as to whether or not the reference to the Council of Florence about the rights and privileges of the Eastern Churches applies to Pastor Aeternus, the document on the papacy. If it is not part of the document I do not see how it is anything less than an interpretive note that clarifies the teaching's place in light of Florence and the historical relationship between the Pope and other bishops as well as between the Pope and the various Eastern patriarchs.
What most reflective Roman Catholics and all Eastern Catholics find troublesome in Pastor Aeternus is not the infallibility portion, but the "universal ordinary jurisdiction" point. "Ordinary" does not mean normal, it means ordinary in the sense that the bishop of a diocese is its ordinary rather than auxiliary. Cardinal Hergonrother's clarifying document Pasce agnos states:
“The Pope is circumscribed by the necessity of making a righteous and beneficent use of the duties attached to his privileges. He is also circumscribed by the respect due to the General Councils and to ancient statutes and customs, by the rights of bishops, by his relation with civil powers, by the traditional mild tone of government indicated by the aim of the institution of the papacy itself: ‘to feed’."
The "customs" and "rights of bishops" have never, to my knowledge, met a Conciliar definition. The bishopric of Constantinople hopped ahead of Antioch and Alexandria at a council in the line of patriarchs. The pentarchy of Rome, Constantinople, Antioch, Alexandria, and Jerusalem was proclaimed at two general councils. Sacramental orders were defined at Trent. Yet no binding teachings—again, to my knowledge—exists in depth about the rights of bishops. Patriarchs are even more difficult because, regardless of their historic value and fatherhood over theological and liturgical traditions, they are human inventions and not divine institutions like the episcopacy and the Petrine succession. The function of prudence is thus difficult to explain.
One must remember that, irrespective of the Ultramontanist fervor of the 19th century, papal "ordinary jurisdiction" can never be normal. Indeed, it is the historical exception, from the earliest days onward. Some interventions were not welcomed, such as the deposition of the imposter Photios from the archbishopric of Constantinople and Clement's seemingly uninitiated letter to the Church a Corinth. Others, like the various judgments over the validity of Baptisms, the admission of controversial figures to Communion, and legal matters, were invited by others, suggesting that the initiating bishops and patriarchs thought the Bishop of Rome both had sufficient power to make episcopal adjudications outside his patriarchate and that such an occurrence was not the norm.
The balance between Rome and the rest fell away for a variety of reasons: the Chalcedonian schism, the permanent alienation of the Greek patriarchate and its re-invention after 1453, the [positive] outcome of the Investiture Controversy, the Reformation, and the loss of the Papal states. As the various non-Latin Churches, with few exceptions, separated from the larger Church, less leverage existed to check Rome's behavior and keep the diversity of traditions at the forefront of her mind. Justinian calls to mind an formerly-exempt bishopric in Spain, exempt in that it was once free of an archbishopric above it until Pius IX gave into regal requests. Local elections of bishops were once approved by the pope and almost always revolved around local candidates. In the modern day, bishop Michael Olson of Fort Worth is abnormal in that he is from Forth Worth.
Neglecting that a balance did once exist and forgetting that human constructs exist in the Church amid Divine institutions (the Papacy and the Vatican are only the most obvious of this interplay) lets one slip into thinking "It's either 19th century Ultramontanism or nothing." This is folly. Prudence. Prudence wins out. Unfortunately, prudence is not a doctrine, nor can it ever be. I would favor a strong, exactingly worded understanding about the relationship between the Bishop of Rome and the non-Latin patriarchs. Would this be a teaching though? I doubt it. Like the pentarchy of yesteryear, it would establish human interactions with Divine things, namely bishops.
In the mean time, read Fortescue's The Early Papacy. It is valuable, not only a historical reference book, but also as an insight as to how the ancient Church understood Rome's role and how popes should behave relative to the universal Church. Lastly, take cues from the ancient church, but do not idolize a golden age. The good Dr. Fortescue said it best himself:
"Go and teach all nations, until Photius is intruded at Constantinople; and I am with you all days, even to the year 451."