In a comment box at the GreenBaggins blog, Jason J. Stellman sets forth a simple but important challenge (link to comment).
The challenge is this (paraphrased):
If "apostolic succession" is the solution to multiple competing Scriptural interpretations, then what is the solution to multiple claims to "apostolic succession"?
Let's suppose for the sake of the argument that there is some ambiguity in Scripture that we would like to resolve. Suppose further that we try to resolve it by resorting to "apostolic succession." We will encounter multiple claimants:
1) Mormons (who claim to have living apostles)
2) Roman Catholics (who claim to have a living successor of the Apostle Peter)
3) Eastern Orthodox (who claim to have a plurality of bishops that have succeeded the apostles)
4) Other "Orthodox" groups, including the Nestorians, Monophysites, etc.
It does not appear that the answer can come from any disputed Scripture, because that would introduce a circle. I have heard some folks claim it is history, but if disputes over Scripture are fierce, disputes over History are often even more fierce.
I would respectfully submit that there is no neat answer to the challenge. By whatever skeptical rule one denies that Scripture is the rule of faith, one's own rule of faith will perish.