Continuity mistake: At the end a shot is shown of the FBI airplane in mid air. The airplane shown is a Gulf Stream V; which has a very distinctive nose. After the scene inside the airplane; another shot is shown of the plane's exterior, however all of a sudden they fly a Gulf Stream 100, which is a significantly larger plane and a very different design. (00:41:05 - 00:45:00)
Revealing mistake: When showing the corpse's neck where the puncture marks are, you can see her pulse. (00:16:38)
Exit Wounds - S5-E21
Factual error: The BAU is called in to assist the Sheriff's Dept. in Franklin, Alaska (a made-up town, although there is a ghost town by that name). By statute, Alaska has never had any Sheriffs. Functions filled by sheriffs elsewhere fall mostly under the auspices of the Alaska State Troopers. Other law enforcement is by community or (rarely) borough which is what Alaska has instead of counties.
Continuity mistake: In the scene where the unsub is having a tea party with her "dolls", look at the diabetic woman's right hand when the unsub is pouring her tea. When the tea is being poured the doll's right hand is palm up. When the camera cuts to a close up of the cup the doll's hand is face down. The doll is paralyzed due to the drugs and had not regained control of her body yet, making it impossible for her to move the hand on her own.
Mosley Lane - S5-E16
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.
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.
Suggested correction: He didn't say George.
Continuity mistake: While George Foyet is stabbing Agent Hotchner, the knife is extending from the handle. The blood is at the top of the blade, and as he removes it, the blood moves to the bottom of the blade, while the top remains clean.
Factual error: They were talking about serial killers having kids on the plane at the end. Hotel said, Manson had 10 or 11 children. Charles Manson only had 3 sons.