Gomer wears a medal with a rifle surrounded by a half circle when he is in dress uniform. Sgt. Carter wears the same medal, but none of the other men in the platoon wear it.

Can someone explain what the medal is, and why Gomer is the only private to have one?

Okay, I looked closely at the pictures in the DVD ads, as well as one episode. Gomer's medal features a pair of criss-crossed rifles, and it is the Marine Corps "Expert Rifleman" badge.

The highest award for marksmanship in the Marine Corps, a Marine wears it for one year, and then he must re-qualify. If he qualifies for a lower award, he cannot wear the "Expert Rifleman" badge until he qualifies for it again.

This does not answer my question about why no one in the platoon except Carter and Pyle are wearing ANY marksmanship badge.

In the last episode, Cpl. Duke Slater is also wearing the same award that Sgt. Carter and Gomer wear.

In the episode "Home on the Range," Sgt. Carter assigns Gomer to fire a bazooka during maneuvers. He explains that thanks to all the possum hinting Gomer had done back in Mayberry, Gomer is an excellent shot.