During one scene aboard the fictional USS Watertown, a crewmember describes the rogue submarine as "diving". However, the other boat was already submerged; that is, it made a dive when it submerged. It's absurd to describe the boat as "diving" while it was already submerged. One common correct description for the action in question is that the other boat "goes deep" or "goes deeper".
At one point during a briefing, Loren describes a foreign submarine as "slightly wider in diameter". The correct maritime term for the width of a ship, even a submarine, is the beam. To sound more authentic and less landlubberly, Loren should have described the vessel as having a "slightly wider beam".
When the crew is in general quarters, they are wearing WWII era steel helmets. The DOD by this time had adopted the Kevlar MICH Combat Helmet, which is nothing like the steel helmets.
Webb says the cruise missile is a SS-25. A SS-225 is an Intercontinental ballistic missile, not a cruise missile. It is a road-mobile missile and most certainly cannot be launched from a diesel-electric submarine. A SS-25 has a 550 - 800 kT warhead larger than a dirty nuke.