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.
Visible crew/equipment: When James Charles, the guidance counselor, says, "It could be someone you know, or it could be a stranger you pass at the grocery store," the actors' red T-marks are visible on the floor at Reid's and Gideon's feet. Then when Charles continues to say, "gathering information on the case," we can also see the actor's white T-mark beside the counselor's feet, where he will stand after he introduces Gideon.
Continuity mistake: When Garcia accesses the bank's page online Prentiss gives her the account number login, 1552 9384 6729, and we see Garcia typing it correctly on the screen with the password, but when it cuts to the account's page showing deposit and balance, we see in the balance box the account number's last four digits are 7629, not 6729.
Other mistake: While Hotchner and Reid are talking about Hollow Man and the Mill Creek Killer, Reid's going through the newspapers and when he figures out that the two killers have been talking to each other via the classifieds, there are two closeups of an ad's text. After Hotchner suggests using their relationship against them, Hotch says that Reid's fake ad will imitate Hollow Man's language patterns to send a message to the Mill Creek Killer. Then we hear Reid reading the fake ad they just placed in the classifieds, but the problem is it's the same ad that was shown in the closeups earlier, plus an additional line at the end - "here's my gift to you."
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.
Factual error: This episode takes place in current Seattle today (no illusions of a "Seattle in this fantasy world") including using Google earth as a means of identifying a specific area of action. But all the street signs in this episode are blue where as all street/interstate signs in Washington State are green with white letters.