Yes, trivia and inconsistencies...
This is the only episode of TAGS where all three Howard men appear: Rance, Ron and Clint.
All of the information originally appeared on imdb.com
Let me preface the following by saying, and it has been said before, back in the 60’s when TAGS was being created, those creating the show had no thoughts that TAGS would have such a following 50+ years later. They also, had no knowledge that “we” would have the technology we have today to dissect and analyze each scene. If so, I suspect “they” would have put more into continuity. They were just trying to make a living and produce a product the public would like.
I have noticed most of the issues you point out. Keep in mind, the scenes are individually filmed(shot), one camera, and not necessarily in chronological order. Regarding the scenes where the ID of the T-men change from one scene to the next then back, I once read somewhere that that took place because of the child actor rule. When Opie was available, the initial T-men were not, thus “they” for the sake of time, just stuck two different guys in the background of the scene.
I’m sure all scenes of an episode that take place in the courthouse are shot at one time while, all scenes that take place on the Taylor porch are also shot at one time, etc, and not in chronological order. Once all scenes are shot, they are then pieced together in the editing process. As you watch an episode, count the number of times the camera angle changes. Each camera angle change represents a different scene. It is a wonder they get anything correct.
When one looks at a scene where you can only see one actor speaking, the actor to whom he/she is speaking may or may not even be in the studio. A good example of a scene where the actor is speaking to another actor, yet that actor is not in the scene. In the episode “Thelma Lou’s Attractive Cousin” when Barney arrives at Thelma Lou’s house, Barney honks, Thelma Lou runs out of her house, leans against the passenger door of the squad car in doing so, covers the door vent window. In the scenes where she is talking to Barney, the vent window can not be seen, yet in the scenes with Barney is talking to Thelma Lou, from the passenger seat and through the door window, the vent window is totally visible. Thelma Lou may not have even been on set when Barney’s scene was shot.
Of course, Shorty, but do you feel TAGS is unique in this way? There were movies back then, not to say years before then. It's fun to notice and talk about, more fun to be sure than seeing all the same episodes cycling over and over and over again. Oh now, did I change the subject? By the by, the windows all over Mayberry had no screens. That would work for a show in Barrow, Alaska where it never gets above zero four months every year, but in North Carolina?