Continuity mistake: When the kidnapper is taking the girl out of the basement, she is barefoot as she climbs the ladder; but when Morgan pulls her out of the car, she is wearing sandals with an intricate strapping pattern.
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: 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.
Plot hole: In the scene where The Reaper/George Foyet calls Haley from Marshall Kassmeyer's home he identifies himself as Victor Collins from the Marshall Service. Later in the episode Hotch calls Haley and tells her he needs Jack working the case. Jack comes to the phone and asks him "Is George a bad guy?" Until Hotch called Haley she didn't know Foyet was not a US Marshall named Victor Collins.