When Andy and Thelma Lou meet for the first time in the cemetery, as they hug, on the far shot Thelma Lou's arm is over Andy's arm; however when the camera view changes for the closeup, Thelma Lou's arm is now under Andy's arm.
Andy and Helen's son, Andy Jr., is never mentioned in the 1986 NBC reunion movie Return to Mayberry. In the movie, Andy and Helen return to Mayberry to visit Opie and his wife, who are expecting their first child. Although the movie shares some continuity with the Mayberry R.F.D. story line, it doesn't include Andy Jr..
When Andy first enters the courthouse to surprise Barney, he walks by the window on his way to greet Barney. Visible through the window is a construction project showing a new building being built. When they exit the building at the end of that scene, the scene beyond the window is now that of a completed structure that resembles an office of some type.
The production crew apparently paid very little attention when they were filming the scene in the classroom (with Barney dressed as a clown). You can see boys sitting in seats with the names "Melissa" and "Annie" on them, and a girl seated in a seat for "Edwin."