Factual error: The show falls into the Hollywood myth on polygraphs. Jesse is given a polygraph test after pleading guilty to the 4 murders. He answers all questions, except the last one, honestly. The 4 traces on the polygraph show no real movement on these questions. On the final question, Jesse lies and all 4 traces spike. If polygraphs actually did that, they would be admissible in court. But the reality is, it is the opinion of a highly trained operator that decides if there is a lie. The average person could not look at a polygraph results and point out a lie. There is no huge, visible spike. The producers could have replaced the 4 traces with a red\green light: Green is an honest answer and red a lie.
Continuity mistake: Sara takes pictures of Brenda with an UV light camera. The camera used to film the episode for broadcast is barely able to show the walls in the background as tiled. When the UV pictures of Brenda are used in the interrogation, the photos show Brenda's back up against the tile wall.