This list does not represent the only errors in this episode. There are simply too many inaccuracies, misrepresentations and outright fabrications to address them all. Viewers would do well to keep the series' disclaimer in mind: this series is inspired by an actual crime, but characters, scenes and dialog are invented "for creative and storyline purposes."
Under the Banner of Heaven: Season 1 E2 · “Rightful Place”
Episode Synopsis: With a lead suspect in custody, the investigation uncovers more ominous questions than answers as the hidden history of the once admired Lafferty family is exposed.
Question: Is having a family tree that goes “way back to the pioneers” considered “royalty”? Does it make you special if you served a mission or started a business?
NOT TRUE: If that were considered royalty, most members of the church in Utah at that time would have been royalty. And going on a mission and starting a business are not all that unique, either. In fact, the young men of the Church are expected to go on missions if they are able.
Question: Do women covenant to obey all men for the rest of their lives?
NOT TRUE: Women were placed under covenant to obey their husband (not ‘all men’) as long as the husband was being righteous. Part of being righteous is to not act like the men in this series are acting towards women. This is explained more here.
Here are some resources to help you become acquainted with the actual event: