Response to a Roman apologist: "an objective authority"

This article, unlike most of what I intend to post, will not be heavily concerned with exegesis of the Scriptures; rather, I'll be looking at the historical separation of the Roman, Protestant, and Eastern Orthodox churches, and some of the Roman and Protestant church's arguments.
There are two common reactive attitudes from the Protestant world towards Roman Catholic teaching: instinctive opposition, and acceptance of their terms for the debate. This article by the excellent theology blog Parchment and Pen attempts to correct the first problem, but errs on the other side by defining the debate in Roman Catholic terms, as though Protestants needed to accept Roman Catholicism in order to accept Roman Catholics as brethren. I've responded in the comments to the original poster's misconceptions (there are some excellent comments in that discussion, as you'd expect when Beckwith becomes involved in a discussion), so I won't recap here; rather, I'd like to respond to a Roman Catholic commenter, "Micah", who accurately and elegantly distilled the issues in a short post; and unlike the original poster he gives criteria for accepting the Roman church's claims.
The question, to Micah, is whether the Roman Church objectively and exclusively has apostolic authority. After some discussion, Micah made an elaboration, which nicely establishes his claim as requiring three points of proof. He explained that the Roman Catholic Church has objective authority because it has unbroken apostolic succession by holy ordination; because it is a single unified institution; and because it is "catholic" (universal) in not being tied to any particular ethnic origin or nation. He identifies how several other classes of local churches might have one, but lack another of these.
We can examine each of these three alleged marks of a true church to see how closely the Roman church adheres to the standard Micah requires of it. We can then examine the teachings of the Church throughout the ages to see whether it is in agreement with the Roman church on what the marks of the true church are.
The following posts, and hopefully comments, will dive into this issue more thoroughly. I plan to post four more posts in this series, but I will alter these plans based on trackbacks and/or comments.