I agree with those who hold the opinion that Jesus was writing the names and possibly specific sins of the accusers in the dust. Not only is there some tradition surrounding this theory, there is some possible light shed in the book of Jeremiah.
O LORD , the hope of Israel, all who forsake you will be put to shame. Those who turn away from you will be written in the dust because they have forsaken the LORD , the spring of living water (Jeremiah 17:13)."Mikveh" is the Hebrew word translated in verse 13 as hope. The "mikveh" is a collection of ritual waters used for purification. This verse implies that the Messiah was to come in the authority of YHWH as a source of living water.
...but whoever drinks the water I give him will never thirst. Indeed, the water I give him will become in him a spring of water welling up to eternal life (John 4:14).I believe these men came with insincere hearts and were attempting to trap Jesus because they had rejected Him as the hope of Israel in their hearts. Jesus was using scripture to point this out to them and convict their hearts.