When Andy and the family get into their car upon leaving church, the Taylor house can be seen just two houses down the street.
It is obvious that Luther is not playing the saxophone. He jammed the mouthpiece into his mouth and it hit his cheek. In another scene, he is supposedly playing but his fingers never move on the keys.
When Andy and the band are rehearsing, they are obviously in the courthouse interior set, modified to hold everyone.
Barney mentions he is able to remain thin because it runs in the Fife family. He then states his mother is the same way, but his mother married into the Fife family, so her weight wouldn't be attached to the Fife's family metabolism until Barney's generation.