The Pharisees tried to use the Law to trap Jesus, but their attempt involved plenty of hypocrisy that resulted in the Pharisees leaving the area. Now it's only Jesus and the woman.
Jesus first asked the woman where the accusers are and if any condemn her (by "condemn", He meant "punish"), and the woman said that no one condemned her (8:10-11). Granted, that does not necessarily mean she did not have any faults (especially in the adultery department), but that means that she does not have to face said punishment.
Eventually, Jesus made a bold statement -- he would neither punish her (8:11). From a legal perspective, this is technically allowed as punishment of normal adultery must involve two people rather than one. Also, Jesus technically had the authority, too (as stated in Deuteronomy 18:18-19). Because of the unjust application of the Law (as well as Jesus's authority and intent), Jesus did not punish the woman. Afterward, Jesus told the woman to not sin (8:11) because sinning ruins lives.
To close off, Jesus proclaimed that he is the "light of the world" (basically a super guide). Following Jesus means having the "light of life" and not "walking in darkness" (8:12). As the ultimate light, Jesus rebuked hypocrisy that results in unjust condemnation and did not punish the woman in spite of her faults. Later on in John, because of the cross/resurrection, Jesus provides the gift of forgiveness in spite of our faults (even though He has the authority to punish) -- and we can believe in Jesus for his gift of forgiveness.
The interesting thing to note about John 7:53-8:12 is that there is some debate on whether or not the section should be in the Bible. Some say no because it does not seem to fit with John's writing style. Others say yes because it flows with the story and that the event actually happened.
Either way, the section has no serious doctrinal counters to the rest of the Bible. The section can be seen as a supplement and supporting evidence of Jesus's character.