Anastasios,
Well the Pope is a bishop--just not an Orthodox one. And Pat Alexy calling him such is not any kind of affirmation of the Pope's Orthodoxy!
You'll have to believe me when I say that what you said here gave me much to think about.
Too often, when we get into these discussions, we end up (due to the categories of thought we've been handed) thinking of these things in a very narrow way.
For example, in one way of speaking, you could certainly say the Pope is a "bishop". The word "bishop" simply means "overseer" (episkopos), just as "priest" is really "presbyter" (elder), deacon "diakonos" (minister, last time I checked), etc. Also, the word "Church" (ekklessia) simply means "gathering", etc.
Obviously, in their own context, the Pope, the heirarchy which is subordinate to him, etc...they all play those roles. The Pope plays "uber-patriarch", his "bishops" actually do oversee a particular territory, and their presbyters really do act as extensions of the episcopal ministry in the parishes. By the strict definition those titles provide, in and of themselves... well, that is going on in the RCC.
However, what does this all mean, when it is all separated from the context of the Orthodox Church? Indeed, what does that term "Orthodox Church" really mean, at it's essence?
You yourself say that the Pope is not "Orthodox" - and I assume you mean this in the genuine sense of the term (not just because he is not "Byzantine rite" which I know is how some people, mistakenly, use the term "Orthodox"), in that he does not confess the "correct teaching", nor do those in his communion (save perhaps for a few extra rowdy, philo-Orthodox Uniates...who always perplex me, but that's another subject.)
However, I am curious to know whether or not you believe the Pope is part of the same "ekklessia", as those who are "Orthodox"? I could not see how he would be, since if the "Orthodox Church" is not, well... Orthodox, in it's confession, what is it? Just a collection of Bishops and their flocks, who just happen to get along, for cultural or political reasons?
And if he (the Pope, and those in his communion) are not actually members of this "Orthodox Church", then what does that make of all of those roles I just previously mentioned. While it's obvious that they (the Roman Catholic heirarchy) act the part of bishops, and have those responsibilities (and are so viewed by their flocks), objectively, what is their status?
For if they are not members of the Church, can they be members of Christ, Whose Body the Church is? And if not members, though regarded as "overseers, elders, and ministers", can said clergy really be viewed as having a participation in the Priesthood of Christ (which is the source of any true Priesthood experienced in the Church - for there is only one Priest, the High Priest, Christ, and one Oblation, not many, as existed under the Old Law)? For does not Christ say in the Gospel of St.John, that He is the "true vine", and without Him we can do absolutely nothing?
This is the heart of the matter, one which I think is too often obscured by dwelling on the most surface, exoteric dimensions of the sacraments and their "validity" - indeed, can we speak of Christian Mysteries as having such autonomy from the Body of He Who is their true Minister?
Seraphim