The Lieutenant takes Washburn's driver's license first, and later takes Belle's license. A police officer does not have the power to "take a driver's license", as only a judge can do this in accordance with the law.
The Lieutenant tells Washburn that he is "Not suspended, but fired". While a superior officer has the ability to remove an officer from service and suspend, they cannot summarily fire the officer. Firing an officer involves a formal hearing before termination can take place.
Washburn opens the valve on a tank of Nitrous Oxide, saying that they can't fire at them because the "flammable" gas will explode. Nitrous Oxide is not flammable but it is an oxidizer. If you lit a match in a room full of N2O the flame would glow brighter than usual but there would be no explosion.
As the blue BMW is waiting during the last bank robbery, a police car passes by to scope the scene. The cop car alternates between being a 1993-1994 Ford Crown Vic, a 1995-1997 Ford Crown Vic and a 1998-2004 Ford Crown Vic between shots.
When Washburn reaches to grab his gun while it is on the backseat of the taxi, his butt gets in Belle's way. However, in one shot of Washburn's side during this scene, we see his butt sticking out the window, but Washburn never moved.
After the second bank robbery, while the women are modifying their vehicle, they are clearly wearing black, flat, men's-style shoes. However, when they pull of their suits only a few moments later, the women are suddenly wearing high heeled sandals.
When Washburn races to get Belle to the hospital Marta is at first sitting behind the driver's seat. However, in the next shot she is seated behind the passenger's seat and Belle is seated behind the driver.
SPOILER. When the robbers get trapped on the freeway segment, one of the robbers fires at Belle, Washburn and the Lieutenant. Two of the rounds hit the cab's windshield and leave definite holes. Shortly thereafter, as Washburn is driving Belle to the hospital, the bullet holes in the windshield disappear and reappear depending on the shot.
Right before Washburn exits the bus and puts on the fake mustache, there is a tall short-haired blonde woman in an army green jacket walking with a large bag. In the next shot from above, she does not appear to have this bag as she goes around the corner.
Near the beginning when Belle gets in her taxi for the first time, she turns her taxi light on, then it cuts to a different view of the car where the light is no longer on, she buckles up, starts the car, and flips the light on again.
When Belle gets her taxi back after being impounded by the police, the previously broken back left window has been fixed. As the police were keeping the car as evidence, they wouldn't have fixed it, or else they'd be tampering with evidence.
In the final chase scene, when the convertible cars jump the gap in the freeway, the gap between the expressway seems huge as the cars jump the gap, but as the shot goes forward and the cars land and skid to a stop on the platform, the gap no longer seems as far apart.
When Washburn and Belle are at the Sanitation Department they say that the garbage man they are looking for is "Anthony Scalia" and show his name on the computer terminal. When they show the garbage man in the next scene, the name on his shirt is "John".
While Belle's driving the businessman from Times Square to JFK airport, the trees dotting the streets, the cleanliness, and the blue street signs hanging from the traffic lights are all dead giveaways of Los Angeles shots.
When Andy hears the radio dispatch about the robbery, he's walking down a New York City street. When he pulls out his badge to stop a car seconds later, he's on a Los Angeles street. The shots of him are in New York, the shots from his POV of cars crashing are in Los Angeles.
When Washburn is with the guys from Cuba in the beginning in the movie, he lies that he is from Havana, Cuba. He said that he lived on the corner of "Castro street", the guys from Cuba say "there's no Castro street in Havana!". Actually in Havana there's a street called F de Castro.
During the exterior driving scenes, the induction plates on the air intake do not move when the engine is accelerated and the car is speeding up. The plates should open up to allow in more air every time the gas pedal is pushed as it is mechanically linked to the pedal.
When Washburn crashes the first car, he pounds on the steering wheel. This action triggers inflation of the airbag. The sensor for the airbag is in the front bumper, which was undamaged as the car ran backwards into the store. Thus, pounding on the steering wheel would not fire off the airbag.
When Belle runs over and knocks down the fire hydrant, water squirts straight up out of the top of the air intake scoop. This would be physically impossible as the water would have to go through the engine first. Additionally, there is no opening on the top of the induction scoop, and any water in the intake would shoot out of the front, not out of the top.
When Belle and Washburn are at his mom's house, she says the words Jungle Fever (1991) thinking that Washburn and Belle were together. If you look closely at Jimmy Fallon's mouth, you can see him mouthing the words exactly as his mother says it.
The goof item below may give away important plot points.
In the last shot when Belle and Jeff Gordon take to the track, you can clearly see that they cars are from different divisions. Belle's is a late model stock car that would run at local tracks, whereas Jeff's car is a Cup car. These cars would not be on the track at the same time.