Which specific sin would that be? Adultery? Is that why the whole crowd went away, because they were all guilty of the exact same thing they were accusing the woman of?
If Jesus meant to specify a particular sin it would have been easy enough to clarify it and the passage simply states that if anyone in the crowd was without sin itself then they could cast the first stone. Obviously, none of them were so nobody was in a position to cast one. Arguing that Jesus was writing a passage from Leviticus in light of that makes no sense.
Appeal to incredulity.
Think about what doser said in post 260, then read the following verse.
‘The man who commits adultery with another man’s wife, he who commits adultery with his neighbor’s wife, the adulterer and the adulteress, shall surely be put to death. - Leviticus 20:10 http://www.biblegateway.com/passage/?search=Leviticus20:10&version=NKJV