In the chase scene, the cars have both a front and back Arizona license plate, but the state of Arizona only issues back license plates.
The truck that almost causes a traffic accident at the beginning of the episode has a black and white UN hazmat placard on the front bumper with the 4-digit code 1263. Sadly, this is a bogus placard. 1263 is the real hazmat code for "paint or paint-related materials", but it should be on a red "flammable" placard, not a black and white "toxic/corrosive" placard.
Reid says that Pheidippides was the first person to run a marathon and Hotch points out that he died after doing it, which Reid says he knows. Except Reid should have known that it wasn't true.
Pheidippides actually ran from Marathon, not a marathon.
Pheidippides also didn't dramatically deliver his message and die, this was just made up decades after his death because it made a better story.
The unsub is driving a black Ford Taurus while Morgan and JJ are in pursuit. He makes an illegal right turn from the middle lane, cutting off a silver Buick sedan. The light is red, which doesn't mean anything to the unsub but the law abiding citizen in the Buick shouldn't be speeding through a red light.
During the chase scene, JJ reads out the plate number as standard English numbers. She should really be using a phonetic alphabet like the NATO Phonetic Alphabet (Alpha, Bravo, Charlie vs A, B, C).