Buford T. Justice's angry, vulgar self could be just a manifestation of his frustration over the three films.
Buford actually is a competent and scary force to be reckoned with to the point that he forced three robbing teens to 'watch the car' until one of his associates arrive. Despite the fact that Frog walked out on Junior, he was notably calm and civil in defusing the situation. As the pursuit drags on and the car becomes a shadow of what it once was, Buford had grown more frustrated to the point that he became more insensitive with fellow state members of the police force, including his son. It could be possible that The Bandit broke Buford's relatively calm demeanor.- More of his facade was stripped away in the sequel as the car gets crumpled, and Buford considered retirement after yet again failing to apprehend the Bandit.
- And again in Smokey and the Bandit 3, where Buford actually felt defeated when his police cruiser once again suffers punishment, and the shark mascot being stolen by Snowman!Bandit. If it wasn't for Junior's ironic Rousing Speech, along with letting the Bandit get away once again, Buford would've accepted retirement with dignity.
Cledus "Snowman" Snow might be a very distant ancestor of Coriolanus Snow, infamous president of postapocalyptic Panem in The Hunger Games (and tribute mentor in The Ballad of Songbirds and Snakes).