A Boy and His X: A boy and his dog, albeit one that had been stolen.
Contrived Coincidence: Rosco takes Flash out of his car and puts her on the ground while he goes to get some water for his overheating radiator, seemingly for no reason except to let the dognappers see her and, thinking that she's Maxine, steal her from him.
Distinguishing Mark: The only visual difference between Flash and Maxine is, Maxine has some dark spots on the underside of her floppy ears.
Happily Adopted: Terry Lee is adopted by Maxine's owners, who can't have children of their own, when they see how happy Terry and Maxine are together.
Heartwarming Orphan: Terry Lee, the adorable red-headed, freckle-faced 7-year-old whose parents were both dead and was emotionally withdrawn ... until he sees Maxine.
Identical Stranger: Maxine, to Flash. Bo and Luke have to inspect Maxine very carefully to see the differences between her and Flash.
Manly Tears: Rosco, as he fears the worst about Flash.
Boss tells the Hazzard County Pound to make money or else they'll be shut down, so they sell their only dog (really Maxine) to the Dukes for $10. When Boss learns that there's a $10,000 reward for Maxine he calls and asks about the dog the tells the pound he's coming right over. Boss hangs up before the pound manager can tell him that the dog was already taken.
What with one thing and another Rosco's dog Flash ends up at the Hazzard County jail. Boss gets on the CB and tries to tell Rosco but Rosco isn't in his car, he's searching for Flash where someone (actually one of the dognappers) told him she had almost hit a basset hound.
Prince and Pauper: Maxine the valuable showdog is virtually identical to Flash, Rosco's beloved basset hound with a more humble background. The constant dog switching briefly leads Flash to a life of luxury.
Unwitting Instigator of Doom: Rosco tickets an out of town van for speeding. This lets dognapped basset hound Maxine escape, which leads to the dognappers stealing Flash (by mistake) and also leading to orphan Terry Lee getting adopted by Maxine's real owners.
uncredited June Foray. Hence Terry Lee sounds almost exactly like Rocky the Flying Squirrel.