Factual error: Many shots of the submarine in drydock show Halifax, Nova Scotia's MacKay and MacDonald bridges in the background.
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.
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.
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)