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.
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.