Revealing mistake: While Andy, Aunt Bee, and Opie are at the Hollywood studio watching a scene being filmed, when Andy mistakenly stands up and interrupts the filming we can see the wall and shelves behind the director, and it should look familiar because it's the wall and shelves from Floyd's shop in Mayberry.
Continuity mistake: When Andy and Floyd stop by Wally's station, Flora's wearing a striped uniform shirt and there are a bunch of cars lined up waiting for service. Then later, when Goober gets back from vacation and shows up at the station, in the first shot of the station Flora's wearing the striped shirt and all the cars waiting for service are the same as the earlier shot, but in the closeups Flora's now wearing a solid color uniform shirt. (00:06:05 - 00:09:20)
Continuity mistake: While Andy and the townsfolk are at the courthouse during the storm, when The Gypsies walk in the two men are wearing wet rain ponchos and the woman is wearing a striped serape, but then she's wearing a wet raincoat, and it switches yet again in following shots. (00:21:45)
Continuity mistake: At the start of the episode, while Barney's in Andy's kitchen he's wearing a shirt with large distinctive designs, but when he and Andy walk into the courthouse Barney's shirt has completely different designs (though it's the same type of shirt). (00:01:00 - 00:04:00)
Revealing mistake: When Andy arrives at the studio for the publicity shots, while he's speaking to Mr. Michaels note that behind them we can see the Taylors' Mayberry kitchen cabinet/counter and a wall with their distinctive gold/silver design wallpaper. (00:03:50)
Revealing mistake: When Andy, Aunt Bee, and Opie are visiting the studio set while the scene between fake Aunt Bee and fake Andy is being filmed in a fake Taylor living room, note that behind the real Taylors we can see bits of the interior of their Mayberry house scattered in the background offstage. Some things to look for include their living room's stone wall with the mantle, their two reddish chairs (one with the fringe at the bottom), and a wall with their distinctive gold/silver design wallpaper. It's particularly funny when Opie looks at the "fake" living room set and comments, "Is that our house? It sure looks different!" while we the viewers can see the "real" Taylor set behind him. (00:20:35)
Continuity mistake: After Opie tells Andy that he knows he'll win at high noon, it cuts to Warren in front of Floyd's shop (with its furniture conspicuously missing), but later when Andy walks over to Floyd's shop its facade has changed. Note differences such as window structure, and the name "Floyd's Barber Shop" painted on the window which wasn't in the earlier shot. (00:18:05 - 00:24:15)
Other mistake: During the scenes at Goober's filling station we can see a few brand names covered. For example, the "Chew Mail Pouch Tobacco" wall thermometer sign has its brand name "Mail Pouch" covered with black tape, and all the yellow "Pennzoil" cans have half the letters of their brand name painted yellow, so all the cans read "en zo."
Visible crew/equipment: When Floyd and the other men are with John Canfield joking about Floyd's barber skills, a chalk T-mark is visible on the ground by the man with his foot on the bench. Then when Canfield walks away we can see more chalk marks on the ground.
Revealing mistake: When the bus pulls up for the Taylor family to leave for Hollywood you can see behind the bus a California freeway with cars moving in both directions. I don't think that Mayberry had a freeway right outside town. The scene is fixed when they return in "Aunt Bee on TV." There has been a tree put there so the road wouldn't show.
Visible crew/equipment: After Goober has deliberately removed the distributor cap from Andy's squad car, when Andy slams the hood shut we can see the reflection of the filming crew on Floyd's window. Then when Andy and Helen drive away in Goober's truck, the microphone pops up into view at the bottom of the screen. (00:17:20)