A fair question. I think you must know the Torah to know the answer. There's two ways, imo, as to why this incident went wrong.
They brought the woman without the man (that was one error that had been made). The Torah indicates that both the man and the woman caught in adultery were to be put to death (Leviticus 20:10). They, however, favored the woman to use to try to accuse the Messiah. They hadn't even gone through with the right procedures. They had only set this up to accuse the Messiah as John 8:6 says. They weren't judging righteous judgment (a Torah requirment, of course, found in many passages).
There is an interesting explanation as to what Messiah was writing on the ground in this passage. It could be very possible that he was writing down the Torah commandments that accused them of doing wrong.
The other one is that (and I'm sure you heard of this one perhaps) that what he was writing was Jeremiah 17:13, where those who forsake the living waters were prophesied to be "written in the earth".
He had been in the Temple the day before, declaring himself as those living waters in the previous chapter (John 7:37-38). So when he came to the Temple again the next day, he could have written down Isaiah 12:3 and Jeremiah 17:13. When those who heard his words ("he that is without sin, let him cast...") after he wrote in the ground , they somehow became convicted in themselves (John 8:9) and walked out. Possibly realizing that before their eyes that prophesy was coming to pass. They had forsaken the living waters.
Either way, the people were at fault, and Messiah upheld the Torah. He asked the woman where her accusers were (her witnesses, since out of the mouth of two-three witnesses is some one put to death - Deuteronomy 17:6), and if no man had condemned/judged her. After they had left, she had no witnesses against her. Messiah didn't catch her himself in the act and even if he had, he was only one witness (and you need at least two). So he said,
"Neither do I condemn you. Go and sin no more". True Torah knowledge and judgment.
If anyone upheld the Torah here, it was indeed the Messiah. Any prophet trying to turn away the people from any of the Torah commandments is supposed to be rightfully condemned (Deuteronomy 13:1-5). Messiah never broke Torah however. He was without sin and without fault before Yahweh's Word. He was put to death wrongfully. Had he been "changing the law" or ignoring it or deliberately breaking it, he would have rightly been put to death. I know that he was sinless, however, and considered all the Word authorative and not an old, bondage document.
: