Factual error: In the scene where 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.

Continuity: After the submarine is hit by the first missile, 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.