He didn't disobey the Sabbath or Moses' traditional law of stoning of a woman caught in adultery? Please explain your viewpoint.
The Pharisees had imposed numerous restrictions on what they considered permissible things that could be done on the Sabbath, so they accused Jesus of breaking the Sabbath because the disciples picked heads of grain to eat. Jesus explained that the Sabbath was made for man, not man for the Sabbath.
According to Jesus' understanding of the Sabbath the disciples did not violate God's covenant.
With regard to the woman accused of adultery it is important to remember that the Mosaic law was based on a presumption of innocence and two or more credible witnesses had to have been witness to the violation. The witnesses were required by law to cast the first stone. All the men left and there was no one to accuse her.
Jesus couldn't accuse her because he was not a witness.