Continuity mistake: In the opening scene (after the credits), Elle's hair is in bangs. In the scene where they discuss the killer using zip ties instead of ropes her bangs have suddenly grown in. (00:05:05 - 00:15:45)
Continuity mistake: In the scene where Gideon realizes the unsub is a cannibal, Garcia enters the office behind him and shuts the door. In the next shot, the door is wide open. (00:13:40)
A Real Rain - S1-E17
Continuity mistake: When Gideon puts on a glove to examine the flint blade from the fourth victim's head, the glove snaps and breaks. In the next shot, more close up, Gideon's glove is not broken.
Continuity mistake: When Reid and Lila are in the pool, kissing, he explains how it is wrong that they are out in the open, and in a pool. Lila then kisses him again, and the paparazzo in the bushes takes pictures. In the first shot of this kiss, a close-up of Reid and Lila, her arms are down by her sides, but when seen through the camera, her arms are suddenly around his neck. Back to a close-up, and her arms are once again down in the water. (00:25:30)
A Real Rain - S1-E17
Continuity mistake: At the end when the FBI is going to the apartment where the killer is holding the hostages, Gideon puts on a bulletproof vest while standing next to the car talking to the cop and a second later while he's walking toward the building he puts the vest on again.
Continuity mistake: In the elderly victim's home, when Gideon is going through the dresser drawers he finds the small frame with the picture of her son, and there is a blue frame lying in the drawer, but in the next shot that blue frame is lying on the dresser even though he never touched it. (00:02:10)
Continuity mistake: In the scene when the investigators at the police station realize who the killer is, the deputy enters and says that a revolver is missing. However, when Cory pulls out the weapon in the woods, he is holding a semi-automatic pistol. The deputy would know the difference between the two, but still uses the wrong term (a revolver may be referred to as a pistol, but an automatic like Cory had stolen can never be called a "revolver", as the chamber does not revolve).
The Fisher King: Part 1 - S1-E22
Continuity mistake: Agent Anderson (who takes Elle to her house) puts on his jacket twice.
Continuity mistake: In the scene just after Gideon talks to Cherish's mother we see him start to walk toward the rest of the team. In the wide shot we see Reid standing with his hands in his pockets and jacket open, we then see him close his jacket and cross his arms as Gideon gets closer, but in the very next shot (the close up on Reid) we see his jacket open and his arms at his side once more. (00:12:20)
Plain Sight - S1-E4
Continuity mistake: At the very end on the plane, Gideon gives Reid the two tickets as his birthday present. In the shot facing Reid, he holds the tickets facing himself. In the reverse shot, the tickets now face Gideon. (00:39:30)
Continuity mistake: Before the BAU catches the serial killer Carl Arnold, they used a heat sensor and it shows five people sitting at a table. They said there were three adults and two kids, but when they break in the house, the mother and one kid were sitting at the table, the father was tied up nearby, and Carl Arnold and the other child were in the basement. They were found by Derek Morgan right before Carl Arnold threw the child at Gideon, who fortunately caught him.
Continuity mistake: At the start, JJ puts a file down on the desk, and her left hand is in front of her, and she has 2 items in her right hand. When the camera angle changes to behind JJ, her left hand is now on her hip. (00:02:20)
Continuity mistake: When Reid disarms Maggie, he has his hand on the gun but no thumb on the hammer. When the shot changes to Maggie's POV, he has his thumb on the hammer. (00:37:20)
Continuity mistake: When Reid tells Lila that her manager is dead, he has his hands on the back of his neck. When the shot changes, his arms are now lowered and under the water. (00:27:00)
Continuity mistake: When Lila gets the note that was taped to her door, she holds it by the side in the close-up showing the contents of the letter and from the top when she is crumpling it up. (00:15:30)
Continuity mistake: When Gideon is talking when we first see him, the pictures behind him on the screen change instantly. It should be noted, that when we see the pictures change, there is the audible click and visual delay of a slide change which is not present on the instant change. (00:04:20)
Continuity mistake: Morgan gets a call from BAU and we see him holding his phone in one hand then two. (00:03:40)
Continuity mistake: When Reid is asked if he plays ball, the way he holds the football changes between shots. In one shot he holds it in 2 hands and in another he holds it in one hand. (00:14:30)
Continuity mistake: When Morgan finds the Glock 19, his grip on the clip changes between angles. (00:14:30)
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.
Bishop73