During Abner's and Sam's "The Country's in the Very Best of Hands" musical number, both Mayor Dogmeat and the podium he's standing behind disappear twice.
When Available Jones goes to open the rocket containing Stupifyin' Jones, he pushes on the side of the rocket to open the doors. However, there is no button or other device on the rocket that he is pushing.
General Bullmoose says about Abner and Ms. Von Climax, "Then, by community property, half of everything he owns, she owns." Community property doesn't work like that. If Abner owns any part of the Yokumberry entity, it's separate property, acquired before a marriage. And he doesn't own it anyway--his parents do.
When Senator Phogbound first arrives in Cornpone Square standing up in the taxi, he waves his hat to the crowd and says "Hello everybody, hello. Glad to see you. He, he. Well now, say.." but his lips don't move to match the words. As he moves forward and greets the townsfolk, the same thing happens, including his mouth making the words "My boy" to Li'l'Abner but there are now no words heard. This mismatch continues until the Senator gets up on the podium to make his speech.
In several shots in the film the top of the backing can be seen, which reveals some of the top of the sound stage and lighting grids.
The top of the scenery and several lights are visible on the upper right throughout much of the "Jubilation T. Cornpone" number, and other scenes in the Dogpatch set.
Studio lights can be seen in many scenes (especially in letterbox).
On at least three occasions during Lil' Abner's meeting with General Bullmoose in Bullmoose's office, the boom mic remains center top of shot as the camera dollies out for a wider shot.
In the final wedding scene, there is a long shot early in the song where the boom mic is plainly visible, well down in the top center, for the entire shot.