Character mistake: Close to the end of the episode, Dr. Reid says to the psychotic guy that was holding hostages, "M-theory cannot be proved." It should be "proven, " not "proved." Dr. Reid is supposed to be a genius, so he should be the last one to make such a mistake.
Other mistake: There is a mugshot of a 35 year old suspect on Garcia's computer. According to what she is saying, the suspect's mother died 10 years ago. A photo shows her with the suspect and he looks exactly the same age as he does now. (00:40:00)
Character mistake: Dr. Reid calls Penelope "Kristy" on a phone call.
Suggested correction: He calls her "Garcia."
About Face - S3-E6
Continuity mistake: This episode is a flash back to when Agent Gideon joins the team, but agent Prentiss is already a member. She didn't join until season 2 (when agent Gideon was already an established character).
Factual error: Violet is seen wearing Hood style flip-flops where there is a denim like covering just beyond the sandal straps, but this scene takes place in 2001, 12 years before those shoes were available.
Suggested correction: It actually looks like she is wearing wide leg jeans which cover her feet and shoes giving that illusion.