How to reconcile the Didache's instruction with Apostolic succession? 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."


  Chap. XV.
  
  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.


http://www.catholicplanet.com/ebooks/didache.htm

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?
Henry Chadwick writes about this in his book The Early Church (Penguin, 1993), on page 50.

First he explains that the role of the "bishop" (episkopos) evolved to be a primus among the elders (presbyters) in the late apostolic or early post-apostolic era. But it would take a while until the bishop received a more formal recognition as a separate tier of leadership. The writings of Ignatios of Antioch thus do not describe a common practice at his time, but something he recommends, and that gradually became accepted as a way to guarantee unity. The pressure from gnostic movements was the primary influencing factor.

The episkopos thus remained a presbyter as well. The first thing that differentiated bishops from other elders, was the power to ordain. He would be the primary layer on of hands, when a new presbyter was ordained, though others might join in.

But when a new episkopos was ordained, all of the other presbyters would lay hands on him, though "some variations in custom appears".


  At Alexandria we are told they did so, until the third century and
  there is no mention of visiting bishops; but in Rome by the time of
  Hippolytos (early 3d century presbyter) only the bishops who came from other
  churches laid hands on the one consecrated, the chief consecrator being chosen
  by the bishops themselves... The actual choice of the candidate rested with
  the whole congregation... Election by the people likewise played a large part
  in the ordination of presbyters and deacons. 


This of course is a secondary source, but from my reading of other books on Church History, the explanation is non-controversial.