Character mistake: When Kim is trying to convince Lisbon to help the FBI on their case, she says Jane stopped the ten-year reign of a mass murderer. Red John was a serial killer, which, by the FBI's definition, is a criminal behavior distinctly different from mass murder; he may have had a large number of victims, but he killed them either one or a couple at a time, with a cooling-off period in between, not all at once.
Character mistake: Towards the end of the episode Patrick Jane plays a game of chess with himself. He moves the queen and states check mate. It is not checkmate, black knight would take the queen in the next move. It is in fact a flawed example of scholar's mate, something that someone of his supposed intellect and chess skills would not be rehearsing.