In "The Guitar Player" (s1e3) and "The Guitar Player Returns" (s1e31), the band leader is named "Bobby Fleet". In this episode, his name is "Freddy Fleet". Writers for the show later admitted they didn't do their continuity homework and made a mistake by naming the character "Freddy". In all three episodes in which the band appears, the Fleet character is played by a different actor.
In most of the episodes in which he appears, Burt Mustin's character is named "Judd". In this one, his name is "Jubal".
At the beginning of the episode, Burly Peters plays for the guys and plays well, but later, when playing in the band, he seems to have no rhythm at all.
When the band makes their return trip around the block, the shot from behind Mayor Stoner, Barney and Andy shows Barney addressing the band in a slouching posture, then in a straight posture with his shoulders back. When the shot cuts to the front, he is instantly back in his slouching posture.
When Andy is shown playing with the band, he is playing a baritone horn with a curved bell. When he walks into the Sheriff's Office in the final scene, he is carrying a case that would hold one with a straight, upright bell.
After the band finishes its march around the block to show off for the mayor, everyone is changing back into their original clothes but the sound of the drum is heard even though the drummer is not playing.