At the risk of being obvious and/or clever, (and with multiple options, a certainty of being wrong) both of which can be dangerous in certain situations, though less immediately dangerous than having a number of hefty stones chucked at you, I submit the following:
By not throwing any stones, the Pharisees are protecting themselves from:
Personal guilt over feeling hypocritical: "I'm killing a sinner, but I'm a sinner too."
Further criticism from Jesus: "He seems to be more preoccupied with making a point and moving on rather than condemning anyone in particular; if I do nothing, maybe he'll shut up and not say clever embarassing things against me which will be repeated by huge crowds. That one little sentence was embarrassing enough."
Each others' death penalties: "Well, suppose I throw a stone anyway, regardless of (H)is disapproval. That will be taken to mean by one of my fellow Pharisees to mean I'm making a claim of perfection. If he does that, someone else will claim I'm claiming to be the Almighty. Too dangerous. Maybe I can stir up trouble for the guy who does throw one."
Supposing that this woman was not Mary Magdalene, which is a separate argument, that would mean that she, to the world at large, has no name, and therefore no particular reason to be heard. After all, she was a woman. Supposing also that there were no other bystanders. Suppose that Jesus wrote something particularly important with a stick. Conclusion: the Pharisees formed a conspiracy to keep it from us. Huz-agh! My first unique conspiracy theory! But I'll go on to disprove it: He was previously teaching people, and they are in the Temple. Plus He used His finger, not a stick. (Lies make the truth more interesting.)
More likely to my mind, He wrote nothing important in particular; He wrote just to perform the act of writing, as opposed to gazing at the woman, the crowd of Pharisees, or any Pharisee in particular. It's probably one of those divine choices we'll never know the why's about, but might be diverting to speculate about, but probably will never achieve the fame of "What did He write?" Was it a distraction for the Pharisees benefit? An act of non-hostility? An invitation for the Pharisees to look downward, which is associated with humility?
To put it simply, my question is: which and/or how many responses was Jesus intending:
shame about killing or hypocrisy
recognizance of also being sinful
paranoia about some new consequences he just invented
reflection upon the words He wrote, assuming He wrote some
just barely enough awkwardness to keep the woman alive