Actually Papal Infalliability only refers to new dogma he creates when "speaking from the throne" it isn't always clear when he was speaking from the throne and when he wasn't. As far as I know only two things have been confirmed to have been speaking from the throne, that of the Virgin Mary, bodily ascending to heaven and something else.
But yes, two popes wouldn't work, because it isn't clear when he is speaking from the throne.
Snapperhead, haven't some pope's later became antipopes having been retracted from the position. Antipope Dioscorus I think, but that was after his death. Celestine II as well, who submitted despite being legitimate.
The pope has done much to being catholicism out of the dark age, although his social stance may be a bit behind, he supports the Big Bang theory and has supported discussions on it in the Vatican.
On that note, any member of the catholic church is able to become Pope, in the 1958 elections (around that time) I think an ArchBishop obtained a few votes. But invariably they elect one of their own to become pope.
Also Tristan he can resign:
§2. If it happens that the Roman Pontiff resigns his office, it is required for validity that the resignation is made freely and properly manifested but not that it is accepted by anyone.
http://www.vatican.va/archive/ENG1104/__P16.HTM