Factual error: Many times the Captain is wearing a red baseball style cap. This is only worn by the Captain when drill is underway to signify, "I'm here, but not really here for the purpose of the exercise."
Factual error: Throughout the combat sequences with the Russian submarine, both the enemy sub and the missiles exchanged between the USS Alabama and the Russian sub are shown as blips on a radar scope. In real life, sonar displays look much different and resemble a "waterfall" pattern that trained sonar specialists can read.
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. (01:09:00)
Continuity mistake: When Denzel Washington meets Gene Hackman for the first time, Hackman is holding a cigar in front of his mouth. In the next shot, his arm is suddenly down on the table, and he lifts the cigar to his mouth again. (00:06:30)
Answer: In the most technical sense ("by the book") it is against policy. But then, the Marines do not allow tattoos and look how well that's enforced. It is up to the ship's Captain to enforce such regulations, and at sea, there's no one to penalize him if he chooses to let the crew smoke at certain times, given certain conditions.
johnrosa