There is inconsistency in the last 4 episodes of the season in regards to school being in session or not. In the previous episode, the kids were excited because it was the last day of school for the year and they didn't have to go back until fall. In this episode, school is once again in session and the kids are told there will be no school on Thursday and possibly Friday because of the 'town business being conducted' (the trial.) The final two episodes the kids are once again on summer vacation and the season premiere of Season 6 is when they go back to school with a new teacher.
In America under the jury system we don't arbitrarily another juror when there is a "hung" jury to get a specific result in the trial.
Andy tells the judge that he might have burned the barn down because he had put the lantern on the post, and he states that the wind was blowing very hard. However, during the entire sequence of Andy going out to the corral, there isn't any wind; not even enough to move his hair.
When Andrew goes to the barn to find the lantern it's almost empty. If it was stocked full the grain would still be there.