Continuity mistake: When the back of the Fratelli's ORV is riddled with bullet holes, you can see they make a distinctive backwards "L" shape above the Jeep letters. Later, when Chunk examines the ORV, the bullets holes are now in different places than they were before. Also, the license plate that is seen on the ORV when it is hit by the bullets, changes design as well.
Continuity mistake: During the jail escape, when Jake is trying to open the locked door, there is a close-up of Mama Fratelli shouting, "Jake, up!" and we see a police cruiser parked on her left. When they leave, in the overhead shot that space is empty, but next shot a vehicle is there, though it isn't a police cruiser.
Continuity mistake: When the first police car makes a U-turn, to chase the Fratellis, the squad car's front passenger window is rolled up, as the officer's hands are on the steering wheel. But in the next interior shot, facing that window, it's rolled down - there's even a black wire hanging over the bottom of the open window, to the left.
Continuity mistake: When Mouth goes down the hole in the fireplace passageway, the cooler base is right beside the fireplace, but when Mikey pushes Data and his backpack into the hole, the base is farther away. When Brand pulls the log holder over the hole the base is back, right beside him, but when Chunk heads for the basement window the base is farther away again.