Continuity mistake: During the briefing Alexei Vostrikov was receiving from the Generals, he has three stars on his shoulders, but for the most of the rest of the movie he only has two stars on his shoulders.
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 one of the scenes where a repair-crew works inside the broken reactor, one of the men can be seen not wearing one of his handshoes. In the moment before and after that, he does wear it.
Continuity mistake: During the rescue scene with K-19, submarine S-270 has 270 painted on one side of the fin and on the other side has 378 painted on it.
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.
Continuity mistake: When the sub launches its test missile you can see the ice around the sub cracking up. Yet later, when the crew is outside playing football on the ice, there are no cracks visible.
Continuity mistake: When the crew is waiting for the confirmation from Moscow to launch the missile, there are 3 lights flashing one after another. Then, when they receive the confirmation, there are two lights on, but in the shot later there is only one on.
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.
Continuity mistake: When K19 is ready for departure from the docks, the flag is waving away from Harrison Ford. When you see overview footage the flag is waving towards Harrison Ford.
Answer: The movie is correct on this. The early Soviet ballistic missile subs like this one had the missile launcher in the sail, carrying 3 missiles. Missile tubes integrated into the hull, and the ability to fire while completely submerged, didn't come til later.