The question of Purgatory, for example, was most clearly defined at Trent using Latin terms, but the teaching of cleansing after death goes back to the ancient Fathers. All Catholics are responsible for upholding the teaching of purification after death, whether explicitly or implicitly, and I know of no Eastern tradition that doesn’t uphold this teaching (what tradition doesn’t offer Liturgies for the dead, or do good works on their behalf?)
On the other hand, nobody is responsible for upholding the specific trappings of these definitions, not even the Latins. It is hardly mandatory for Latins to believe in a literal “fire” in Purgatory, even though Western Councils used such terminology at times to define Purgatory. It is for this reason that the Catholic Church can say that we hold the same Faith with the Oriental Orthodox concerning the nature of the Incarnation; the Orientals use the “miaphysite” terminology and approach, while the Eastern and Latin Catholics use the “duophysite”, terminology and approach, yet we confess the same Faith upheld by Chalcedon that Christ was one Person, both human and Divine.
The only reason we use specific theological models and terminology is because our human minds must convey theological ideas in ways we can understand, and that requires systems and formulas. This doesn’t mean that a given approach is best suited for every theological question, and no human mode of understanding can ever encapsulate God. In every Dogma we are bound by the Truth underlying the terminology, not the human terms themselves.
Non-Latin Catholics must take seriously those things formulated in the West, even if the approach isn’t part of their tradition. Likewise, Latins must take seriously those things upheld in the East even when they aren’t expressed in a manner consistent with Latin tradition. For example, no one in the West can deny that we have a real participation in the Divine despite the fact that this hasn’t been formally defined as such in the West. In the East, however, this was a central controversy that required clarification by Council, and hence the Palamite debates. The issue simply never came up in the West, however, and no Catholic theologians denied that Grace is a real participation of Divinity (the Council of Trent dealt with the issue in an off-hand manner because it related to debates against the Protestants, but it wasn’t a direct issue as it was during the Palamite Councils).
So no Latin can deny real participation in the Divine because it is a Catholic Truth; a Truth defined in the East while never having been a dogmatic issue in the West. It’s binding in the West simply by weight of Tradition, where in the East the Tradition was in dispute; should it ever become an issue in the West I’m sure we’d look to the Eastern Councils for guidance on the matter. Likewise the non-Latin Catholics should take very seriously everything taught at Trent, not because there was a Protestant Reformation in the East, but because it represents a Catholic response to such an event.
IMO, the whole question of what is “binding” and what isn’t is a rather silly obsession, as if we can simply ignore those things that don’t fit neatly into our modern categories. It smacks of the very legalism that many non-Latins accuse Latins of all the time, in fact. I prefer to say that all Churches in Communion must uphold the same Faith, no matter the differences in approach or expression, and sometimes this means that certain issues are simply left in the shadows, not because of utter disregard, but rather because of general inapplicability; they can be regarded as being implicitly upheld by virtue of Communion, without the need of explicit adherence to alien theological approaches.
As for matters of “dispute”, I think that polemics have no place within a Communion. A Latin has no place denying theosis as a heresy, and a Byzantine Catholic likewise has no place decrying the filioque; our traditions may approach these issues from wildly different directions, but we can’t be in Communion while accusing each other of heretical errors.
Peace and God bless!
No, seriously, I was trained on Eastern Syriac (being a Chaldean). I have not reached the fluency level, but I can manage to read Eastern Syriac slowly, but faster than Western. Also, I’m still learning many of the vocab words.
I mean I love the simple and uncluttered Estrangela script, especially for titles, but it’s harder to pronounce, being without the vowel sounds (unless of course one knows the words ahead of time 
).