The Andy Griffith ShowGoofs
There are discrepancies as to the marital/family status of Floyd the Barber. In The Jinx (1962), Floyd mentions having a son named "Norman". In "Those Gossipin' Men", his son appears playing saxophone. And in other episodes, Floyd mentions being married. However, in Floyd, the Gay Deceiver (1962), the premise of the episode is that Floyd is single and finds a companion through a "lonely hearts"/"pen pal" service. But in that episode, there is no mention of his son or that he is either divorced or widowed.
It's been established that the Mayor's Office is above the courthouse and jail. However there is no indication either inside or outside the courthouse that there is any access to the Mayor's office from the street level or inside the jail. At one point early in the series there was a door to the left of the jail cells which was later removed that could have been an access to the upstairs offices but since no one was ever seen using it and it was later removed from the set, there's no way of knowing. In The Beauty Contest (1961), Ellie and Andy depart from a meeting in Mayor Pike's office through the side door of the courthouse. From this episode we can infer that there are steps inside this door that lead upstairs to government offices on an upper floor. However, in most other episodes this door just enters into the back room of the jail.
In North Carolina, sheriffs are independently-elected county officials. Their duties include providing law enforcement to unincorporated areas. A town, such as Mayberry, with a mayor and council would have its own police force. A sheriff is not responsible to county officials, let alone to a city official such as a mayor.