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.
Factual error: Many shots of the submarine in drydock show Halifax, Nova Scotia's MacKay and MacDonald bridges in the background.
Visible crew/equipment: In the scene at the end in the cemetery, you can clearly see the reflections of the boom mic and camera in the shiny brim of one of the guy's hats.
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 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.
Other mistake: In all scenes where the submarine is running on the surface the surface search radar is rotating CCW (viewed from above). All surface search radars rotate CW.
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.
Factual error: The film takes place in 1960, but the propaganda film shown by the Political Officer includes TV footage from the Civil Rights demonstrations in Birmingham, Alabama in May 1963.
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.
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. (01:42:07)
Factual error: When the rescue sub pulls up to the K-19 to begin offloading the crew, the rescue sub is a NATO Oberon class sub, even though it was meant to be a soviet submarine.
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.
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.
Plot hole: How can they have gotten confirmation to launch the missile from Moscow if the insulation on their transmitter was damaged? If it was a separate transmitter, why not use it in some way to contact Moscow during their crisis?
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.
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. (01:55:15)
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.