Other mistake: When Prentiss and Morgan are trying to figure out how the victims were controlled, Prentiss phones Garcia to find a drug that would temporarily paralyze or subdue. Then just as we hear Garcia answering the call, there's a close-up of Garcia's computer screen and we see the picture of five suicide notes, and at this point there have been six victims. Then later, after the seventh victim is found, when Morgan holds the latest suicide note in the close-up, we can see it's the same note that's already been shown.
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Other mistake: At the start, the soon-to-be victim gets off the A train at Spring Street (subway heads south, then Bklyn/Queens) and stands on the west-side platform, facing the southern subway exit, then the unsub comes up from behind him, shoots him and he falls toward the same way that the unsub walks - the southern exit. However, when Hotchner plays the NYPD's surveillance footage, the victim is facing the northern subway exit when the unsub comes up from behind him, shoots, and he falls toward the same way that the unsub walks - this time the northern subway exit. Interestingly, neither are flipped shots since we can see "Spring St" correctly. Later, when Prentiss reviews footage it's as it was shown originally.
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Other mistake: When the character is buried alive the psychiatrist pours bags of dirt on the head of the victim. First, there is a pile of bags that shows only 8-10 bags of dirt, which is not enough to fill the hole. Secondly, the victim was conscious and standing up with no apparent broken bones, which means she could have just stood on the dirt as it was (very slowly) poured in. Additionally, she was buried completely during the entire time the murderer was evading police, having a conversation with Hotchner, and jumping to his death. Then the BAU talked about their suspicions she was still there and had to make it all the way to the basement. She would not have had a "faint pulse" after all of that time.