In light of the selection of a new Pope, this would be a good time for those who don't know much about church history to do some research. One step to take would be to read First Clement. It's one of the earliest extra-Biblical Christian documents we have, and it represents early Christianity in the city of Rome. It has a lot of relevance to the claims of Roman Catholicism.
I've written about some of the inconsistencies between First Clement and Catholicism in the past. See here regarding the papacy, for example. On justification, see here. Or here on Purgatory. Other examples can be found in my collection of articles on Catholicism here or by searching the Triablogue archives in general.
"Some scholars anachronistically saw in the epistle [First Clement] an assertion of Roman primacy, but nowadays a hermeneutic of collegiality is more widely accepted." (Thomas Halton, Encyclopedia Of Early Christianity, Everett Ferguson, ed. [New York: Garland Publishing, Inc., 1999], 253)
"This [the literary genre of First Clement] is a form of address that is identified in rhetorical handbooks and found in other texts that are contemporary with 1 Clement. It is used by those who wish to persuade others to reach for themselves a successful resolution to difficulties that they face, not to force them to submit to those who offer them this counsel….He [Clement] hopes to persuade because he cannot compel or command, and he knows that he cannot take it for granted that those whom he addresses will welcome and act on the counsel that he gives. He avoids the use of the imperative, and speaks instead in the second person plural….The second corollary is confirmation that this letter [First Clement] offers no evidence for the primacy of Rome at the time of its composition. The church at Rome writes to the church at Corinth of its own free will, but the form in which it does so makes clear that it could not take for granted that its counsel would be either welcome or in any way binding at Corinth. Nowhere does the Roman church demand obedience to its own authority, but only to that of God, as revealed in the Greek Bible and in certain Christian texts and traditions." (Andrew Gregory, in Paul Foster, ed., The Writings Of The Apostolic Fathers [New York, New York: T&T Clark, 2007], 26-28)