In the ancient world, trials could take place anywhere, but they typically took place either on the steps of the temple or the gates to the city. This case probably happened in a public place, partly because of the use of the word contend which is normally associated with contending in the gates. In addition, if Jacob and Sherem had simply conversed in private without public witnesses or observers, the pro-Sherem portion of the populace may have suspected foul play when Sherem fell helplessly to the ground. Nobody said, "What happened to him?" So it would seem that there were people present who knew, when Sherem fell, that the will of God had been manifested. And someone needed to care for him and keep him alive "for many days" after he fell to the ground (7:15). In addition, there would have been less reason for Sherem to have made a public retraction, had he not made a public accusation. His final confession was more than just a confession; it was an attempt to undo the damage that he had done. He had probably spoken out on many occasions; he probably had a following, so there was a great likelihood of this involving some of the public.
Nowadays, we recognize a professional judge by the robes he wears. There was no professional judiciary in the ancient world. Every man could be called to sit on a panel of judges, rather like our juries are. People who happened to be at the town gate could be impaneled and sit as a judge on that case. Trials usually were short. They would never go over a day or two long. If they did not have the necessary witnesses, the court would simply adjourn and give people time to bring the witnesses, but typically, cases in the ancient world probably lasted only a couple of hours.
Jacob was wise. He knew he would be unable to persuade Sherem, but Sherem also was skilled; he presented his case competently and sufficiently to call the question. Sherem probably knew that he would have to go through some kind of ordeal to seek validation of his claims and to substantiate his accusations.
Sherem accused Jacob of the capital offense false prophecy (Deuteronomy 18:20), likely on several grounds. This was a capital offense. Second, he also accused Jacob of blasphemy. The crime of blasphemy was narrowed by later Jewish traditions and law, so that that only speaking the holy name of God out loud qualified as an offense, but in pre-exilic Israel, blasphemy could mean a broad range of insolent or seditious statements; anything that was demeaning of God, of the king, or the leader could qualify. Even a slave could blaspheme the master by speaking insolently. It was a very serious offense, as we see when Abinadi said that God would come down and suffer, a very unflattering statement about God, and so the priests of Noah accused Abinadi of blasphemy on that very ground. Blasphemy was also a capital offense, under Leviticus 24. Third, leading people into apostasy was another accusation that Sherem levelled; it was also a capital crime under the Law of Moses (Deuteronomy 13).
So, Sherem accused Jacob of three capital crimes, and I guess he figured that all he had to do was win on one of the three. Sherem may have felt certain that God would sustain him. However, God does not support the wicked, and we know how the story ends. If Sherem had won, there likely would have been friends of Sherem who would have executed Jacob. But the way it turned out, in many ways, must have become a foundational precedent at the beginning of Nephite legal history which would affect the next 400 or 500 years of Nephite history until the coming of Christ.