When Sheriff Droopy Cathcart is leading Bo and Luke into Colonel Claiborne's office, he isn't wearing his hat. When the scene goes into Claiborne's office, Droopy is miraculously wearing his hat, like he had never taken it off.
Morgan Woodward, who plays Colonel Clayborne in this Cool Hand Luke themed episode, actually appeared in the original movie playing the sinister Boss Godfrey. Boss Godfrey was referred to as "the man with no eyes."
Slater: You should bring your cousin around here more often. I'll give her a little rough housing.
Luke: Slater, you said something about going a few rounds. How about right now?
When Colonel Claiborne says "What we have here is a failure to communicate" he's taking the line directly from the movie Cool Hand Luke.
James Avery, who appears as one of the convicts, would go onto play Phillip Banks on The Fresh Prince of Bel Air.
The basic plot of Cool Hands, Bo and Luke is taken from the classic 1967 movie, Cool Hand Luke (starring Paul Newman and George Kennedy).