Sgt. Carter is listed as having won the WWII Victory Medal. Yet in the show it is stated that he has been a marine for 14 or 16 years. Since the show started in 1964, he would have joined the marines sometime after 1948, too late for the WWII medal.
Throughout season 1, the length of Sgt. Carter's career in the Marines varies from 14 years to 18 years.
Sergeant Carter's rank is E-7, or "Gunnery Sergeant." As a Marine Gunnery Sergeant, he would be called either "Gunnery Sergeant Carter", or "Gunny Carter," not "Sergeant Carter."
When wearing uniforms with ribbons, Carter often wears an Army Good Conduct Medal ribbon (which is awarded for serving at least 2 years or one year in combat). This is probably an homage to actor Frank Sutton's WWII Army service. However, he does not wear a Marine Corps Good Conduct Ribbon, which is authorized for 3 years of active service. As a Gunnery Sergeant and Drill Instructor, he would have served over 3 years active as a Marine - hence, earning the award.
When Gomer, Sgt. Carter, and the majority of the other Marines are wearing their green fatigues, the shirts have "V" shaped pocket flaps that cover the buttons and have the Marine Corps emblem and USMC on the left pocket. Slater though always wears a fatigue shirt with square pocket flaps, exposed buttons, and no emblem, etc. on the left pocket, indicating this is not a USMC fatigue top but one from another branch of service (sometimes other "extra's" are seen wearing the same top, but rarely).
The outdoor backdrops in Gomer's interior barracks scenes do not coincide with the actual outdoor scenes when the platoon is outside in formation. In the interior, other rows of barracks are clearly seen directly across from Gomer's barracks. But when the shots are taken outside at a distance, no barracks are seen.