Gomer has a bandage on the middle finger of his right hand when he is shoveling the sand pile that wasn't there just previously in the barracks. When he comes in to see Sgt. Carter after he gets his phone call the bandage is gone again.
The TV show is being shown in color when it is obviously a black and white set having no knobs to adjust the color or hue. Also the antennae isn't extended yet the picture is crystal clear as if it's hooked up to cable which didn't exist at the time.
The jacket (shirt) that Gomer gives Aunt Bee to wear while cleaning doesn't have the USMC emblem on the left pocket. This is also evident with some of the other Marines when they're lined up by the "nice" Sgt. Carter and again while watching TV in the barracks. Some have the emblem while others don't. In such a extremely regimented organization such as the Marines is they should conform with each other.