• If this is a set-up, then to set this up would have involved a lot of stepping over one’s conscience: This would mean they assembled intentionally in large enough numbers. They would have to find an adultery that they could catch at a convenient hour (which means that it had been going on regularly, and they didn’t interfere, didn’t warn, didn’t counsel, didn’t prevent). Yet with all that to catch an adultery “in the very act” as they claim would have mean stalking, waiting, observing. Not a nice business.
• Another issue is that though an adultery is by definition an act committed by two people, they let the man go and hold on to the woman. In a worst case scenario, the man acted knowing about their intention to discover them. But even if not, the Law of Moses clearly stipulates that both man and woman are equally guilty and liable to punishment (Deu 22:22). To apply a law selectively is a form of injustice already.

But what exactly is the trap they set up for Jesus with this?

• The trap is that Jesus, by claiming to be the Father’s representative (which he did multiple times in Jhn 5-6), he now cannot go against God’s law. And the law says to stone adulterers. So if he doesn’t push for a stoning, he contradicts his claim of being a representative of his Father in heaven, and with that much of his earlier teaching. If he doesn’t defend the law, his righteousness and authority is in question.
• Another issue: Jesus had come to popularity at least partially by the tremendous grace and freeing acceptance that he had shown to all, especially to those on the fringes of society. By forcing Jesus’ hand to push though a stoning of the woman, the scribes and Pharisees would have accomplished at least their goal of breaking Jesus’ popularity, of putting his grace into question, of forcing him to negate his earlier behavior.
• Yet to force him to push through with a stoning is a trap in one more way: According to Roman rule, death penalties can only be given by Roman courts and meted out by Roman officials. The Jewish council was given the right to judge minor cases, but it was not given the right to pass death sentences, far less to implement them. This can be seen in Jesus’ own trial, where they cannot implement the death sentence without Pilate’s consent.
• But now: according to Roman law adultery is not illegal, it is not a crime punishable by death under Roman law. So by stoning the adulteress Jesus would become guilty of a crime under Roman law, guilty for an unauthorized killing, a full-on murder. Murder on the other hand was a punishable offense under Roman law. If Jesus pushes ahead the stoning of the woman, he then becomes guilty of murder under the Roman law, and they can accuse him for that!
• The falseness of the position they put Jesus in also lies in the fact that the Jews have not meted out death penalties for adultery for centuries. Yes, it was God’s law originally, but they have long departed from that. God allows them to change the law if they so desire, as can be seen from the transition of Israel from an elective and representative government to a monarchy in 1 Sam 8. God warns them and counsels them to not do that, but when they persist, he lets them do it.
• Or another example: When David commits adultery with Bathsheba (and also murder of her husband Uriah), he does not execute himself for either as should have been done if the original Law of God was still in place.
  Another example is Joseph, upon finding out that Mary is pregnant, he doesn’t push for a stoning, as is stipulated for the adultery of an engaged person (see Deu 22:23-24), rather he plans to dissolve the engagement without further ado and is called “righteous” for that in Mth 1:19.