The bible verses associated with this is often the woman accused of adultery. What most commentators fail to mention is the legal aspects of the witnesses who are required to testify. Two or more witnesses were required for a criminal charge and a witness had to have integrity. Also, the witnesses were required to throw the first stones.
When Jesus asked that those who are without sin to cast first stone, he was proving that the woman could not be found guilty under the law.
Also, weren’t the Philisines who brought the woman to Jesus trying to catch Him being contradictory about what He taught? I was under the impression that this example really has little to do with judgement.