Continuity mistake: In S1E9 Randy asks Earl what animal he'd want to be. Earl says he'd rather be a dog than a cat because he is allergic to cats. However, here Earl is shown around cats with no allergic reaction. Instead, Randy is the one who has allergies.
Continuity mistake: Whenever Earl, Joy and Randy go to visit Jasper in the flashback, his Russian bride is in the background. She shouldn't be around at this time as earlier in the show Jasper is barely introducing the gang to his Russian bride years after the flashback occurs (S1E12).
Continuity mistake: Randy spray paints his name over the bargain buys logo on the side of the truck. However, when Earl and Joy realise there is a man in the back of it, it cuts to a long shot and it still has the bargain buys logo on it. Then when Earl comes back with the gas, Randy is painting over his name with the white paint.