As it pertains primarily to Catholicism, Eastern Orthodoxy, and other large denominations that not only lay claim to an unbroken successive line, but who also put significant emphasis on it:
The Didache instructs congregations to "elect" Bishops and Deacons "for themselves."
Elect therefore for yourselves Bishops and Deacons worthy of the Lord, men meek, and not lovers of money, and truthful, and approved; for they too minister to you the ministry of the Prophets and Teachers.
My initial understanding of this would be that these communities are in charge of [democratically?] naming their own clergy. That in itself isn't terribly contradictory sounding, but there's no mention of any formal process or Church approval -- let alone a consecration of the "elected" by the Church. The omission of such formality in what appears to be a very formal and detailed early "Church Handbook" seems to call into question the notion that a strict Apostolic Succession was present in the early Church.
In the very least, one might wonder whether some congregations in the early Church did elect their own Bishops, without pre-approval or education by the Church, blurring the line of succession.
How do we adequately square the Didache's instruction with Apostolic Succession?