Character mistake: After the murder that takes place while the team is at the church meeting, they gather together to talk about narrowing down the suspect list to the people who didn't show up to the meeting. Spencer shows up with a stack of papers and says 18 suspects didn't show up. We then see his actor break character and almost laughs when he looks over at Ashley, whose actress too almost breaks character from laughing.
Character mistake: In the initial meeting at FBI headquarters, the agents mention the Zodiac killer. Gideon says about him "Yeah, and he killed for 30 years without being caught." In actuality, the Zodiac's known victims were killed between 1966 and 1970. In letters to the public, Zodiac claimed responsibility for several other murders (most of which were solved without being attributed to Zodiac), but no later than 1974. Gideon's statement was off by at least 22 years.
Character mistake: Derek Morgan says that he discovered the body of a dead boy in 1991 when he was 15 years old. Later on, you see Garcia searching the computer for personal info on Derek Morgan. According to the computer; Derek Morgan was born in 1973 which would make him 18 years old in 1991, not 15.
Character mistake: Morgan asks Reid what track on the CD (Some Kind of Monster by Metallica) would help an insomniac sleep. Reid replies with "Enter Sandman" however, Some Kind of Monster doesn't feature the song Enter Sandman. (00:29:00)
Character mistake: Reid tells Mrs. Hillridge that he's been working for the BAU about five and a half years, which is roughly since the pilot aired in 2005. But flashbacks in "Tabula Rasa" show that Reid was a relatively new rookie in 2004, which is roughly six years. Considering Reid has an eidetic memory, the six-month discrepancy is a bit suspicious.
Character mistake: In this episode the unsub is copying the murders of Jack the Ripper (with men as victims). The Unsub also taunts the police and BAU with letters, even using the Dear Boss salutation. The BAU draw upon the Dear Boss letters from the original Ripper case as part of their profiling - not only of the unsub but also the Ripper. Handwriting comparisons has shown that the author of the Dear Boss letters was most likely a journalist and not the Ripper. Whilst the unsub may have been ignorant of the forgery status of the dear boss letters, you would expect the BAU to be wiser.
Character mistake: When Reid realizes who the unsub is, he asks Hotch if he was introduced as "Doctor" or "Agent". As explained in the pilot (and in every episode since), the team has always introduced Reid as "Doctor", to make sure that the people they meet treat him with respect and don't just see him as a kid.
Character mistake: When the unsub puts the lock on the woman's collar, he hooks it onto the part where a leash would go. She could easily take the collar off. Later, the lock is on a different hook that is pushed through the collar, so she would not be able to escape. (00:19:10 - 00:33:30)
Character mistake: When Reid and Rossi propose the theory that Kate knew Syd and Jimmy before her disappearance, and JJ expresses her skepticism, Rossi retorts "they're handsome, charming, 19." But while reviewing the case on the flight to Maryland, JJ mentions that the boys are both 20.