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.
Visible crew/equipment: When Elle arrives back at her home the camera pans and you can see the face of a man in the mirror. A man who is not the Fischer King as he has no facial burn marks on him. Potentially simply a stand-in for the character or the actor without the makeup as when the Fischer King is going to shoot Elle you cannot see his face.
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)Ssiscool
Continuity mistake: At the start we see Spencer explaining to Gideon about the Boston Strangler, his orange shirt is untucked at the front with both sides of his shirt being visible. Camera shows Gideon walking off and now only 1 side of his shirt is untucked. (00:05:10)Ssiscool
Continuity mistake: They keep showing the aerial view of one type of jet (such as Gulfstream 100 with its rectangular windows), but the inside shots are always in a "heavy" Gulfstream (such as Gulfstream IV or Gulfstream V, which have round windows). Also, the tail numbers (the N-numbers written on the engine) are always different in the aerial views. Some end with GV, some with SP etc.