Pat Hingle (Col. Tucker) actually fought in the Korean War. After first serving on the destroyer USS Marshall during World War II, he later returned to the military during the Korean War as a boilerman technician in the Navy.
Captian Hunnicutt refers to the "Perils of Pralines" after playing a joke on Major Winchester. This is a riff on the often-rebooted "The Perils of Pauline" (1914, 1933, 1947).
Col. Potter refers to Father Mulchahy, who is wearing a woman's robe as "Gorgeous George", a real life pro wrestler with a gimmick of an effeminate man. He wore women's robes and make up and would prance around in an effeminate way. He began this gimmick in 1941 and kept it going for the rest of his career. His gimmick had varying influence on the gimmicks of many pro wrestlers to come, such as the late Adrian Adonis.
The title is based on April Fools' Day or All Fools' Day which is celebrated on April 1 and is marked by the commission of hoaxes and other practical jokes of varying sophistication on friends, family members, enemies, and neighbors.