Factual error: As I've seen posted, the conning tower (a more correct term is "sail") of the sub is damaged by the sea presure, and later appears intact. In fact, this kind of damage at the place that is shown in the movie should not happens because the sail is a "free flooding" structure: the pressure is the same inside and outside the plates, and only the watertight structures housed in the sail (missile tubes, periscopes and masts, access trunk, etc.) have to withstand the sea pressure.
Continuity mistake: When we first see Alexei Vostrikov, he is wearing a gold wedding band on his left hand. Russians wear their wedding bands on their right hand. The next couple of scenes in which we see Alexei's hands, the ring is correctly on his right hand. Then it disappears completely for most of the film. When he is suiting up in his dress uniform near the end of the film, it is back on his right hand, and remains there for the rest of the film.
Continuity mistake: In the opening sequence, during the missile drill in dry dock (the one that fails) we see one of the engineers open the missile tube to examine the missile. By this point, the exterior hatch has been opened, and daylight is quite visible within the tube, yet moments later Liam Neeson's character climbs out onto the conning tower revealing that its night time outside the submarine.
Factual error: When the General's black Russian car ("Volga" car) stopped near "Soviet NAVI headquarters" and General is entering the house, those who can read Russian can see that this is "Frunze's Museum of Russian Army" - it's just an ordinary Russian museum in Moscow and has nothing in common with the government.
Factual error: At 300 meters, we see the hull starting to cave in - from the outside. But the outside hull is only a cover. The preasure hull is below that. There is water behind the outer hull, so it would never cave in that way. We actually see the double hull in a shot where we pass from the inside of the boat through the double hulls and out into the sea.
Add timeJacob La Cour
Continuity mistake: When the boat has surfaced in the ice, Polenin goes to his cabin. Inside we see a stack of books lying neatly on a top shelf. However, after all the bumps seen during the earlier fast ascent, where things and people were thrown around, the books would be scattered over the floor.
Add timeJacob La Cour
Factual error: Vostrikov is a Captain 2 rank, however when Polenin is about to tell him that they have been found by a friendly submarine Vostrikov's sleeve briefly reveals that he has 4 thick gold bars on his wrist. This is consistent with a Captain 1 rank. Vostrikov would as a Captain 2 rank have 3 thick gold bars and 1 thin.