Colonel (actually Lieutenant Colonel) Watson's cap is lacking the gold braid often referred to as "scrambled eggs" on the visor. Only Lieutenants and Captains would wear a cap with a plain, black visor.
Although Gomer pronounces the "s" in 'Marine Corps' phonetically, it's actually pronounced without the "s" sound, as in 'core'.
Sgt. Carter tells the recruits to take their hats off because they're indoors. At the same time, he's wearing his hat inside the barracks.
Obvious backdrops outside the barracks.
Just after the Corporal calls the barracks to attention, a crew member is visible at the lower left, next to a bunk.
In a scene that is typically edited out of syndicated reruns, Gomer tells Andy that the Marine recruiter advised that he would be traveling to East Asia while in the Marines. During the "Gomer Pyle, USMC" series run, however, Gomer is never depicted in any such deployment.
Gomer tells Sgt Carter that he doesn't have much of a singing voice. It's already been established that he has a beautiful singing voice.