It seems that both Orthodoxy and Protestantism -- from the opposite sides of history -- object to this authority on the same grounds and, in practice, hold a similar conception of the laity. Over on this side of the 500 years we call it the "priesthood of all believers."
As do we. Have you heard of the sensus fidelium ("sense of the faithful"), which was re-emphasized by Cardinal Newman? Pope John XXII was soundly and successfully rebuked by the masses when he temporarily espoused belief in a false doctrine. St. Catherine of Siena, St. Bernard of Clairvaux, and St. Francis of Assisi rebuked popes, and their advice was respected and heeded (St. Francis, however, was ordained as a deacon - not as a priest -, so technically he was not a layman). These saints were the most revered Catholics of their time (one might think of Mother Teresa in our time).
I'm sure there were also many instances of morally inferior popes (e.g., during the Renaissance) being soundly rebuked by holy priests and laymen. This is nothing novel whatsoever in Catholic ecclesiology. No one knows better than Catholics the distinction between the nobility of an office and (too often) the sanctity of the person holding it at any given time. Of course, this has always been the case in the Church and amongst the Old Testament Jews (one need only recall Moses, David, Judas, and St. Peter himself).
Prior to the dogmatic declarations of both the Immaculate Conception and the Assumption of the Blessed Virgin Mary, each pope had received millions of letters, almost unanimously espousing and urging the declaration of both proclamations. Canonization works largely the same way, by means of an overwhelming consensus of both clergy and laity.
The pope does not act in isolation, as some sort of arbitrary dictator. That is a caricature of Catholic doctrine. He works closely with bishops, priests, nuns and monks, synods, Councils, and the laity. The Catholic Church is a Body with a head, not a head without a body, or a body without a head, as in Orthodoxy :-). And, as has been pointed out, much of the conservative, traditional, orthodox movement in the Catholic Church at present is centered in the laypeople (e.g., Hahn, Kreeft, Akin, Madrid, Howard, Keating, many many amateur apologists, the pro-family, pro-life, politically conservative, and home-schooling movements, etc., etc.).
Also, we recognize the sacrament of baptism, and of marriage in many cases, as performed by Protestant clergy who are not ordained by the Catholic criteria, whereas many Orthodox (how many?) don't recognize either our baptisms or yours.
Of course, I realize that the Orthodox would probably object strongly to any association with that doctrine. I am merely drawing a parallel. What is common in the objection to the to sharp distinction between the priesthood and the laity that seems evident in the Catholic church and has perhaps led to a weakened body.
I must vigorously disagree. I maintain that the clergy-laity dichotomy applies equally if not more so to Protestant churches. Your average evangelical or fundamentalist pastor exerts far more high-pressure influence day-to-day on his congregants than the pope does on us. And that would be fine, except that, too often, pastors become the focus of the church to such an extent that, when he leaves, there is a "succession crisis" and a split in the congregation. I've personally witnessed this three times, and each scene was very ugly (and, by the way, I took no part in these fiascoes whatsoever). So if Protestantism is supposedly typified in practice by the "priesthood of all believers," why is that?
Catholics, by and large, don't go through these silly, man-centered crises of personal preference for one pastor over another, etc. When the priest in my parish left (after about 32 years), there was not the slightest ripple of controversy as the new priest came in, and this is how it should be. Priests are more or less interchangeable in this sense, because they aren't the center of attention in the Mass. The Blessed Eucharist and the Lord Jesus Christ present in the Eucharist is, rather than a man and his sermon.
See also the follow-up, much more in-depth piece:
Written in 1997 by Dave Armstrong.