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: Reid says that it's been speculated that Mary Jane Kelly was murdered in a flat rented by the killer - this is completely incorrect. She was murdered in her rooms, where she'd been living since early 1888.
Answer: "The Boogeyman", s02e06. Spoiler alert: The kid is Jeffrey Charles and at that point he had already killed 3 other kids. Jefferey basically hated and resented other kids after his mother abandoned him and his father spent a lot of time with other children because of his job. Jeffery would lure kids Into the Woods and then beat them to death with his bat just because of hate, no particular "reason." The scene you're describing, Jefferey agrees to walk Tracy home when her "buddy" leaves her (at this point the FBI announced there's a serial killer on the loose and kids should walk with a buddy). Jeffrey gets mad at Tracy for walking too slow and for complaining, and he takes a swing at her, causing her to flee Into the Woods and have Jeffery chase her.
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