Adam had a clear conflict of interest taking the case since he was already working with Nels.
When Adam accepts Nels as his first client to check on the background of Mr. Mills land and later decides to represent Mr. Mills as his client, doing so would be a clear legal conflict, which would prevent him from representing him.
During trial, Mills is called to the stand by the prosecution. This is a clear violation of the 5th amendment to the constitution. A defendant in criminal court can only be called by his own lawyer. He can be compelled to testify in a civil matter. But since Mills later laments prison time he may have to serve, that indicates this is a criminal court.
Ice blocks were always stored in ice houses packed in sawdust or straw as insulation. The ones in Walnut Grove are not.
Mrs Oleson is wearing the same red and green dress that Laura is wearing at her very first teachers job, and later as well.
Twice during the trial scene, when the crowd reacts to a surprising statement, the same murmuring sound is used. Both times a woman is heard saying "I know, I heard that."
It would make no sense at all for Adam to start a private law practice in a tiny rural village like Walnut Grove, where most of the inhabitants were poor farmers and unlikely to be able to afford or need a lawyer.