When Uncle Jesse is driving his white pickup, it is very obviously in 'Park'
After the boxing match, Luke is wearing a yellow robe, but in stunt driving scenes the character is clearly wearing Luke's standard blue shirt.
When Boss Hogg & Roscoe walk over to Boss Hogg's vehicle trunk after the fight to notice the trunk open and the fight money missing you can see a sound stage in the background. Then when the camera pans to just Boss Hogg you can see a sound stage in the background as well.
Safety glass wasn't invented till the mid 1900s, so there is no way that either one of Boss's antique mirrors would have been made with glass that would shatter into tiny less-hazardous squares that "spread instantly" across the entire surface of the mirror when one part got struck. The glass would have made long jagged shards like normal window-glass.
Boss Hogg is standing much closer to the mike than Cletus is, yet his fairly-loudly-spoken request to Cletus to act as Luke's referee does not sound over the P.A. system, even though Cletus's "accidental informing of the crowd about Boss's dishonest plan" comes through loud and clear.