Factual error: When the Captain (Gene Hackman) is getting ready to address the crew, the Chief of the Boat (an enlisted man) is briefly shown barking orders to the crew wearing a combination cover with an officer's golden chin strap. A Chief Petty Officer wears a black chin strap. Contrary to popular belief, it's not illegal to wear an accurate uniform on film, in fact the military offer their help to ensure uniforms are accurate: http://www.defenselink.mil/news/NewsArticle.aspx?ID=516, so that's not the reason.
Factual error: Throughout the movie, everytime some type of casualty occurs or an alarm sounds, police type lights go off throughout the ship. Submarines don't have flashing lights or grated decks for that matter throughout the ship. The sound of the alarm is enough, since there are no deaf personnel on board a submarine.
Continuity mistake: After the submarine is hit by the first torpedo, all the crew are picking up things that have fallen down in the underwater turbulence. Then when the captain returns to his personal cabin, all his belongings (most noticeably on his desk) are all in position as though the attack never happened.
Factual error: At one point a character sneaks through the bowels of the ship from one end to the other. This would be hard to do since he would have to pass through the lower level reactor compartment. Even if you could do this (there is no such passage on any nuclear sub) it would not be very healthy.
Factual error: At one point, the US sub's starboard (right) side is shown to have an American flag painted on the hull near the bow. The flag's blue field is at top/left when on this side of any vehicle, it should be at top/right. Proper display of the flag requires the blue field always be located 'forward' of the remainder of the flag on all vehicles, be they plane, boat, tank or even space shuttle.
Deliberate mistake: During the part of the movie where the USS Alabama is sinking deeper into the ocean a shot of the depth gauge was made showing the sub passing 1800 feet at a quick rate. About 20-30 seconds of shots were shown after this to further dramatize the peril of submarine and then the scene cut back to the depth gauge. This time however, the gauge was moving much slower and only shown the sub had sunk 15-20 more feet without any reason for the sudden slowdown in decent.
Character mistake: At the end of the movie, Ramsey and Hunter begin a conversation about Lippizaner horses. Ramsey says they are from Portugal, Hunter says they are from Spain. However, the Lippizaner horse's place of origin is believed to be in modern day Slovenia (though they are believed to have descended from Spain in the distant past). Lippizan is Slovenia's national symbol. Plus Lippizans are associated with the ‘Spanish Riding school' but the ‘Spanish Riding School' is situated in Vienna, Austria.
Continuity mistake: When the incomplete second EAM is shown in the movie for the first time, its subject line states "nuclear missile launc..." However, when this same message is finally received at the end of the movie the subject line states: "terminate launch all missiles". If the first one had been consistent with the second this would have made quite a difference.
Continuity mistake: In the scene where the "Alabama" dives, what we see isn't a ballistic missile-carrying submarine (SSBN), but an attack sub (SSN); actually more than just one, since the masts and periscopes keep going up and down in different shots. It seems that the navy wasn't too willing to cooperate in the production of a film depicting a mutiny onboard a nuclear sub, so the shots were "stolen" from a helicopter in the vicinity of some navy base.
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Revealing mistake: After the XO orders all stop, we see a close-up of the ship's yoke being pulled back. The next wide shot shows the interior as the bow of the sub is rising, and just before this shot ends, note the console that the man with headphones is working at. A pair of crewmembers cross paths in the foreground, then the entire console wobbles, proving it isn't attached to the floor at all.