When the reaper, posing as a motorcycle cop, pulls the couple over, he asks for license, registration, and proof of insurance. In MA, proof of insurance is not something that is required to show as it is stamped on the registration. Also, when the BAU team is looking over the bodies, they notice that the man's license and registration are out of his wallet. In fact, in MA the registration is something that is kept in the glove compartment at all times.
Just before Diane Lanessa is shot by the Reaper, she is seen cranking as the window moves up as if the car had non-powered crank windows. Yet the car that they are in is a 6th-generation (XV40) Camry, which would've had power windows as standard equipment.
Early in the show, a couple in the Boston area is at the side of a dark, country road with two flat tires. The woman in the car is phoning for help and says they're on "Rt. 128." In reality, Rt. 128, also known as I-95, is not a country road but an interstate with 3-4 lanes in each direction.
Rossi describes the Reaper as being a Hebephile, which actually means he has an attraction to young girls just going through puberty (11-14). This is incorrect, the Reaper shows himself throughout the show to actually have Ephebophilia, a condition in which adults are attracted to girls from mid to late adolescence (15-19).