Continuity mistake: Kurt is still recovering from the beating he took in the previous episode with bad cuts on his forehead, checks and temple area. They are red and impossible to miss while he is in the police station. The cuts have miraculously disappeared in the next scene when he goes to visit Mona.
Character mistake: The FBI team responds to a murder crime scene. The victim is lying face down in the bed with blood everywhere. The team leader takes the victim's wrist with his bare ungloved hand. A trained FBI agent would never touch a murder victim without gloves - one to protect himself and two not to contaminate the crime scene. (00:10:00)
Continuity mistake: When Jonah confronts Meyer after the death of the surgeon, Meyer's holding a drink in his left hand as he turns to face Jonah. The shot changes angle and the drink is suddenly in his right. (00:48:40)
Angel of Mercy: Part Two - S1-E4
Character mistake: When Lenore Osgood is speaking on the phone with Charles Wainwright about killing Dr. Hanover, she mispronounces "Larynx" as "Lar-nix."
Factual error: Paul tells Shea that he has a condition called Sporadic Fatal Insomnia. Later, Shea finds a fork in a bag labelled Abby. Paul explains that Abby is his daughter, and he wants to test her DNA, because she has a 50-50 chance of contracting the disease. This is false. Sporadic Fatal Insomnia is not hereditary. Fatal Familial Insomnia is genetic and is the inherited form.
Continuity mistake: Throughout the series, the Barbers pull their cars straight up their driveway. But the cars are nearly always shown coming back down the driveway driving forward.
Chapter Five - S1-E5
Factual error: Pete uses the term "throwing shade" when talking to Perry Mason in the middle of the episode. As this show is set in 1932, the phrase "throwing shade" did not yet exist (the phrase was first introduced in the 1990s). (00:35:00)
Suggested correction: The phrase was not first introduced in the 1990's. While it did become popular in the 1980's, the idea of "throwing shade" as an idiom would have been around before then. A variation of the idiom is found in writings from the 1800's, for example "Mansfield Park" by Jane Austen.