Deliberate mistake: After having wrestled with Santini in his office, Col. Virgil Hedgepath tells Santini, "And no more assaulting corporals in the latrine." Marines use the naval term "head" in refering to the restroom, and would never call it "the latrine." However, since "latrine" is better known to civilians, this could be a deliberate mistake by the film makers.
Factual error: When Santini is reporting into Beaufort, he refers to the Marine behind the desk as "sergeant." However, the rank on the Marine's sleeve indicates he is a Master Gunnery Sergeant. Unlike in the Army, referring to any rank other than E-5 as "sergeant" is considered an insult in the Marine Corps, and no Marine would ever refer to a Master Gunnery Sergeant as "sergeant." The proper form of address would be "Master Guns," "Master Gunny" or "Top."
Factual error: When Ben and Mary Ann are leaving for the prom, their little brother Brian is wearing a vest adorned with various fighter squadron and jet fighter emblems. When he leans around the pillar to tell Mary Ann she looks pretty, you can see that the patch on the lower left is for the F-14 Tomcat. While the movie is set in 1962, the Tomacat didn't have its maiden flight until 1970, and was not put into service until 1974.
Factual error: The opening dog fight scene the Navy F-4's have a Marine squadron designator on the aircraft... VMFA 251 (Vertical Marine Fighter-Attack). Navy fighter squadrons use simple VF (vertical fighter).