Days of Wine and Roses - S5-E11
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.
Continuity mistake: Jane ordered the leather couch he is later seen napping on for the office in a previous season when he made a deal to be able to get a couch (only upper-level officers were allowed to have couches). Since this episode was a flashback to the first time Jane met and worked with the team, the couch he falls asleep on would not have been there, as that event had not yet happened.