In the scene where Dewey crashes the tow truck, the first shot of his face is without blood. The next shot after that when he looks out at Raylan, his right nostril is gushing blood.
In the bank robbery scene, where the getaway trucks' rear tires are shown burning rubber, the very next cut scene shows the driver floor the gas, then they show the tire spinning, and completely out of sequence, they show the driver pulling the column gear select all the way down, which would be a forward gear, and then they show the truck driving in reverse because the front bumper is the last we see of the truck before the following cut scene.
Raylan shows Dewey a letter as proof that the Mexican government wants to extradite Dewey from the United States to face murder charge. The text in Spanish, however, is announcing an annual police conference and its themes. Raylan knows that Dewey can't speak Spanish so he held up something official looking to spook him.
When Dewey gets run off the road by Raylan and Raylan slams Dewey's face into the steering wheel, Dewey says that Raylan broke his jaw. If indeed Dewey's jaw were broke, there is no way he would be able to talk. However, it has been established that Dewey is an idiot and also believed his kidneys had been stolen and later that he had four kidneys, so his medical knowledge is lacking.
During the bank robbery when the driver is told to "Go", you see him step on the gas pedal, and you see the wheels start to spin and smoke. The next shot shows the driver pulling the shift lever from Park, down into Drive. How could the wheels spin if the truck was in park while he was stepping on the gas?
When Dewey Crowe is released from Manchester prison, the sign behind him incorrectly reads "Manchester Federal Correctional Institute" instead of Institution. Additionally, the actual sign outside the prison reads: "Federal Correctional Institution, Manchester."
After kidnapping the Mexican Federale Officer, Raylan drives him to an isolated area on Texas Farm-to-Market road 498. FM 498 is a very short road and is located in a very flat coastal plain region of South Texas that is primarily flat farm land and well cultivated. There are no hills.