Factual error: Lieutenant Hudner comments that he went into the Naval Academy right after Pearl Harbor. Pearl Harbor happened in December 1941 and he couldn't have gotten into the Naval Academy until 1942. Then he says, "The war ended a month before he graduated." The Naval Academy is a four-year school. That means he wouldn't have graduated until 1946, a year after the war ended.
Character mistake: While discussing his squad providing air support for the Marines on the ground, Lt. Cmdr. Cevoli refers to the men as "soldiers." Marines are not called "soldiers" because they are not in the Army. It is common for a layperson to make this error but nobody in the U.S. Navy would do this.
Other mistake: During the brief for the Yalu River bridge attack the Corsair pilots are told to suppress antiaircraft so the "Panthers" can then safely go in to take out the bridge. But in the attack scene, the other aircraft are not Panthers but Douglas Skyraiders.
Continuity mistake: At the bar in Cannes, Jesse pins his pilot wings on Tom so he can make an impression with a lady. A Marine comes over, threatening Jesse. Tom comes to Jesse's defense, and he no longer has the pilot's wings on his uniform. (01:07:54 - 01:10:08)
Revealing mistake: During the battle of the Chosin Reservoir, just before VF-32 comes in to provide air support, the Marines are firing their M1 Rifles. One of them mimics the recoil of it but we don't see the bolt move back when he fires his rifle. The M1 Rifle or Garand is semiautomatic, and the bolt moves back each time the shooter pulls the trigger.
Factual error: When Lt. Tom tries to make up for reporting the insubordination of Ensign Brown during the bridge attack his insignia is only one bar but should be two bars for a lieutenant.
Suggested correction: Technically, it's not incorrect to call him a Lieutenant. His rank is Lieutenant Junior Grade (marked by a single Silver Bar), and a 1st Lieutenant is marked by 2 Silver Bars. The term is usually transparent amongst this rank, it's not uncommon for a LTJG and a 1LT to both be called a Lieutenant.