As Homer drives back from the hardware store and loses the bumper with the BBQ attached, the next scene shows the bumper still on the car.
A wheel is among the pieces of the barbecue pit Homer frantically tries to assemble, but the front of the box shows that the pit is not movable, and has no other obvious functions that would require a wheel.
Homer picks up a shotgun and cocks it, making the conventional "click-clack" sound. However, the shotgun is a double-barreled side-by-side model. Double-barreled shotguns don't have a cocking mechanism. This is a common mistake on "The Simpsons".