Other mistake: At the beginning when Festus rides up and finds Riley Sharp handcuffed to the hitching rail, if you notice the handcuff chain is draped over the top of the hitching rail and there is nothing preventing him from sliding the chain off the end of the railing.
Factual error: Dragon's dog, a Rottweiler, was not in the US until 1931, much later than the show.
Suggested correction: The Rottweiler is considered one of the oldest breeds. It was only in 1931 that the American Kennel Club recognized the Rottweiler as an official breed. There's a difference between a breed existing and being recognized by a kennel club.
Continuity mistake: Marshall Dillon buries an outlaw at Sarah's place. He installs a wood cross at the grave. Sarah comes out and they talk. When she leaves, the scene cuts back to Dillon and the cross is missing.
A Quiet Day in Dodge - S18-E19
Other mistake: Festus returns from catfish fishing carrying a gunny sack full of fish that is bone dry when it should be dripping wet or at the minimum damp from the fish.
The Fires of Ignorance - S20-E17
Continuity mistake: When the school teacher is questioning the father in court, he places a farmers' almanac on the judge's bench and walks away leaving it. When camera cuts to the judge with a clear shot of where the almanac was left, it is not there. (00:44:00)