In John 8, were the scribes and pharisees guilty of the sin of Fornication / Adultery? The Lord Jesus said, "He that is without sin may throw the first stone." Since all of the accusers went away beginning with the oldest, does that imply that the scribes and pharisees (accusers) guilty of the specific sin of Adultery / fornication?


  If there be any of you who is without sin, without sin of this nature, that has not some time or other been guilty of fornication or adultery, let him cast the first stone at her.


Or, does Jesus mean in that instance that only he who has no sin at all, may throw the first stone?
The phrase "he that is without sin" is a translation of a single Greek word, anamartetos, which means sinless or faultless or without flaw.

It does not refer only to fornication, Jesus is effectively saying let the perfect one among you throw the first stone. 

What happened next is that the scribes and pharisees went away. It is not clear whether they ever had any intention of stoning the woman in the first place. The reason they brought her to Jesus was to test Him, to see what reply He would give. If He said she should not be stoned they could accuse Him of going against the law, but if He said she should be stoned He would lose His reputation for gentleness. St Augustine, in Tractate 33 on St John's gospel said


  if he shall approve her being stoned, he will not show his gentleness; if he consent to let her go, he will not keep righteousness. But, say they, that he may not lose the reputation of gentleness, for which he has become an object of love to the people, without doubt he will say that she must be let go. Hence we find an opportunity of accusing him, and we charge him as being a transgressor of the law: saying to him, You are an enemy to the law; you answer against Moses, nay, against Him who gave the law through Moses;


So Jesus in allowing he who is without sin to cast the first stone meant he who was perfect, not simply anyone who has never committed adultery or fornication. In going away the scribes and pharisees were not making a public admission of adultery - if  that had been Christ's meaning the result could have been different.