Once again, Red makes a war reference implying he fought in WWII. In other cases, he clearly states having served during the Korean War.
[EDIT]: In the episode, "Long Away", Red appears in his Navy Dress Blues. The sleeve insignia indicates that Red was a Chief Boatswain's Mate (BMC). On the left forearm are 3 diagonal "hash marks". In the US Navy, each hash mark indicates 4 years of service. Red's 3 hash marks indicate 12 years of service, making it possible that Red served in *both* WW2 and Korea.