When Hotchner puts the cuffs on Darrin Call, he cuffs his hands behind his back. Later when Tommy is talking to Darrin in the FBI SUV, his hands are folded in his lap in front.
Darrin goes to his psychologist, denoted by the therapist's name and "Ph.D." on the door, asking for pills. Psychologists cannot prescribe medication.
Both the FBI and the news channels refer to Louisville Police as "Louisville Police Department" or Louisville PD. In actuality the police in Louisville are referred to as LMPD or Louisville Metropolitan Police Department.
The pharmacist can't remember the name of Call's doctor because he shot a bullet through her computer. Morgan and Hotch walk away, disappointed. However, judging by the angle and location of the bullet hole, the bullet only went through the computer's power supply and out the side. It didn't hit the hard drive (which is presumably where the name of the doctor is saved). This means that the information should be very easy to recover, and Hotch and Morgan should know this.
The unsub is captured in a house that is right across the street from what appears to be a school. In several frames the children are seen playing outside on a playground. However, if this situation had happened in real life, most likely, the school would have been locked down for safety purposes and the children would not have been allowed outside.
When The Reaper tells Hotch "The hard part is not passing out from the pain" you can see that the knife he is pulling out is a trick retractable blade.
In one of the scenes with Penelope Garcia, the type of keyboard she uses, (flexible, waterproof, "Virtually Indestructible Keyboard"), doesn't make clicking sounds. While you can hear clicking as she appears to type.
At the end of the show, the camera points toward the school and you can clearly see a Washingtonia palm tree which could not grow outside in Kentucky.