The Old Testament law stated that in capital offenses, the primary witness was to cast the first stone at the point of execution. (Deuteronomy 17:7) In the story of the woman caught in adultery (John 8:1-11) Jesus refers to this point of law when addressing the woman's accusers, however He reverses the rules for this occasion.
In verse 7, He says,
He who is without sin among you, let him be the first to throw a stone at her.
In other words, He gave the right to begin the execution, not to the one who witnessed her sin, but to the one who could look at this own life and witness no sin there. John goes on to tell us that after these words, there was no execution that day. This acknowledgment of personal sin is very helpful for those who have a "critical" nature.
First of all, it forces critical people to see that finding fault with others is very easy. The difficult (and worthy) task is to examine ourselves in order to discover our own faults.
Secondly, when we focus on our own faults, sins and weaknesses first, it becomes easier to offer mercy to others. After all, it is difficult to refuse to someone else the very thing we grant ourselves in the same situation.
Finally, recognizing that all are sinners, including ourselves, will make it easier to leave the judging to God. When critical people understand that they have no right to judge because they are guilty of the same sins, a tremendous burden is lifted from their shoulders.
So next time we see a person caught in adultery or any other kind of sin, we should remember Jesus' admonition to the execution squad. Let's be quicker to look into our own hearts rather than looking around for rocks to throw.