When Carl Brashear is in his hospital bed, in 1968, Admiral French and Captain Hanks wear the Navy Sea Service Deployment Ribbon. That ribbon was established in May 1980, and made retroactive to August 1974.
The pay grade of Senior Chief Petty Officer was not created until June 1, 1958. Service-wide exams were conducted for eligible Chief Petty Officers on August 5, 1958. The first batch of Chiefs to be promoted to Senior Chief occurred on November 16, 1958.
In the initial scene in the barracks, a modern fire extinguisher is hanging on the wall in the background. At the time the barracks would have had either a water bucket or a more primitive extinguisher.
Everybody in the movie has embroidered name tapes on their uniform shirts and trousers. That wasn't fully implemented until 1999. During the period in which the movie is set, names would have been written in black India ink using a stencil. Sometimes it was scrawled in marker.
Throughout the film, sailors salute chief petty officers and address them as "sir." Enlisted personnel only salute and address officers as "sir." A sailor addresses a chief petty officer (senior enlisted person) as "chief," "senior chief," or "master chief," not "sir."
At the beginning of the final diving exercise, the big Navy clock says 2:00. A few hours later, when a diver comes out of the water, Sunday says that he's been down for over four hours. The next scene shows a nervous Jo waiting for a phone call from Brashear, and the clock says 3:40.
While Carl puts his wedding band with his tags, he takes off his ring, removes his tags from around his neck and puts them on his chest. Nothing is around his neck. In the next shot, the tag chain is around his neck. In the next shot, he puts the ring on the tags and puts the chain back around his neck.
Near the beginning of the movie, young Carl's father plows a field. While insisting that young Carl go to school instead of helping him plow a field, Carl's father places the long leather rein that controls the mules over his head, with half the rein under his left arm. In the close-up shot, the rein appears around his neck, with no portion under his left arm.
When Chief Carl Brashear arrives to the diving school, MM1 Dylan Rourke spits on Breashear's boot and trousers, clearly staining it. When Chief Carl Brashear enters the barracks, his feet and trousers are clean.
The news report in the film says that three 50-Megaton nuclear warheads were lost in the accident, two were immediately recovered, and the third was being searched for. In real life, four Mk28 bombs were lost in the accident, three were located almost immediately, and the fourth was searched for. They were gravity bombs, which fall freely to earth, not warheads, which are carried on missiles. Their largest possible yield was 1.45 Megatons. The only 50-Megaton bomb produced was the Tsar Bomba, a prototype tested by the Soviet Union on Oct 30, 1961.
Carl Brashear recovers a Hydrogen bomb. The newspaper that Billy Sunday reads says "A-Bomb recovered." In civilian and military parlance, a Hydrogen bomb is called H-bomb, and an Atom Bomb is called an A-bomb.
The anchor device denoting rank on a chief petty officer was shown being worn parallel to the front edge on a long sleeved shirt worn with a tie. It was actually worn pointing towards the tip of the collar only on a short sleeved shirt with no tie.
The bomb was found at 2500+ feet by submersibles. Recovery was attempted but failed. The bomb was re-located at nearly 3000 feet by submersibles. Hard-hat diving was limited to 350 feet, therefore divers could not be used in the recovery until it was raised to about 100 feet by submersibles, so divers could attach recovery cables to the bomb and raise it from the water. The recovery ships were USS Petrel and USS Cascade.
When Jo meets Carl, she says that she hasn't seen her father since she was 9 years old. When she comes to the Navy bar, she tells Carl that she pulled her father out of enough bars and she couldn't do it anymore. It's highly unlikely that she was pulling her father out of bars at such a young age.
People often shown saluting while not wearing a hat. Sailors and Marines do not salute while uncovered. The only exception is when in the company of Army or Air Force people, who do salute uncovered, because it might appear discourteous.
When Brashear swims from the U.S.S. Hoist, shortly after jumping in, a sailor has a Number 1 Mark III Enfield rifle. While it was in use at the time, it was a British rifle, and the United States did not field it.
Chief Sunday is reduced in rank to "Petty Chief", which does not exist. He would most likely be "Chief Petty Officer." All ranks of Chief are classified as "petty officers." The lower grades are "third class petty officer" (E-4), "second class petty officer" (E-5) and "first class petty officer" (E-6), then "Chief" (E-7), "Senior Chief (E-8), and "Master Chief" (E-9). A one step reduction in rank would make him a "Senior Chief," but the latter two ranks did not exist before 1958. The senior Master Chief at a command is the Command Master Chief. On a submarine he is called "Chief of the Boat." The rank requires special training.