Woman caught in adultery
Bible commentator Ken Collins suggests:
The trap is this: under the Roman occupation, the power of capital punishment was reserved by the Romans for themselves. All capital cases had to be referred to the Roman authorities and the sentence had to be approved before it could be carried out. So Jesus' enemies figured they could trap Him in a dilemma by presenting Him with a clear-cut case where the Jewish Law demanded the death penalty by public stoning. If Jesus deferred to the Romans, He discredited Himself as a Teacher of the Law. If He condoned the stoning, the Romans would consider Him an insurrectionist and put Him to death. Either way, they thought, He couldn't win. He would either lose His credibility or His life; either way, He would be silenced. 
As it turned out, Jesus simply turned what they were doing back on them. "Let he who is without sin cast the first stone." As the others left, only Jesus remained. He was without sin, but would not bring the punishment of the law against her, telling her instead to go and sin no more.
Historians and scholars agree that the story of Jesus and the woman caught in adultery (John 8:1-11) is not authentic and was added decades later to the Gospel of John by scribes. The story was almost certainly added for the purpose of liberal ideology: if no one who has sinned should cast the first stone, then the message is that no one should punish or even criticize sinners. It is also clear from the writing style that this story was added later.2
2 - Page 63-65, Misquoting Jesus (2005) by Bart D. Ehrman