As the blue Caprice is shown driving towards Washington DC, it has a different license plate number than it does during the rest of the film.
During the course of the film, the Caprice variously has, then does not have, a wheel cover on the front left wheel.
John and Lee go for a run just before meeting Ray in his truck. The run begins with Lee on John's right, but midway through the one-way run Lee is on John's left and Lee's shirt is frame-reversed, although the runners are still running toward frame-right.
As the blue Caprice is driving towards Washington DC, the road signs indicate it is traveling eastbound on Interstate 66 through Virginia. But if they were driving from New Jersey (as the plot implies) to Washington DC, they would most likely be driving southbound on Interstate 95 from the direction of Baltimore MD. They would be nowhere near Interstate 66 or Virginia.
John is shown living with his kids in the US. In reality, John Muhammad had lost custody of his kids after fleeing the country with them. He was apprehended trying to re-enter the country and his kids were returned to the custody of his ex-wife, Mildred Muhammad.
Lee is shown meeting John after moving to the US. In reality, Lee and his mother first met John Muhammed in Antigua.
Lee is shown moving to the US and while his mother stays behind in the Caribbean. In reality, it was the opposite: Lee Malvo's mother illegally immigrated to United States and left Lee behind.
Ray in the film is white, but in real life he was black.
When Lee is walking toward the Army recruiter, a Lexus RX SUV is seen. The film takes place in 2002, and the model shown was not produced before 2003.
The army recruiter is wearing an ACU uniform, which was invented in 2004 and not widely used until 2006.
Early on the movie setting moves into Tacoma, Washington (state), where the character Ray is introduced driving his white pickup truck with a Washington plate. John soon buys a car with New Jersey plates and modifies the car in Ray's driveway. At no obvious time the main characters shift their spree into the Washington, D.C. area, making it very unclear whether Ray and his family had moved to the east coast.