When Alexei Vostrikov arrives to the meeting with the Admirals his rank up to this point is that of Captain Second Rank. However, during the meeting he wears the shoulder insignia of a Captain First Rank. In the next segment when he boards the K-19, he once again is a Captain Second Rank.
When the K-19 is preparing to leave her berth for the first time, the order "single up all lines" is given. This order means that one set of lines is removed, but the boat should remain secured to her berth with a 'single' set of lines. When the order is given, the crew removes both sets of lines, and the K-19 departs.
At the beginning of the movie, Vostrikov wears his wedding ring on his left hand. In later shots it is on his right hand as is customary with Russians.
When the submarine is taken down to 300 Meters during a test dive, prior to the missile launch, we see the side of the sub beginning to crush in from the pressure where the large numbers are located on the hull. Yet these large dents are not seen anywhere else throughout the rest of the movie.
At the beginning of the movie, when the radio officer checks for Moscow's confirmation during the drill, the close-up shot of the radio panel shows the green light active and two white lights active. A second later the radio panel is shown again (which should look exactly the same as no actions were taken), this time the two white lights are inactive, and a third light is active.
The movie presents a fictionalised account of the real K-19 event, however, eight men died as a result of radiation exposure not seven.
The submarine, on its way to fire the test missile, is shown speeding through the water with bubbles coming from the propellers. This is called cavitation and creates LOTS of noise. A stealthy submarine, on its way to a launch, would never cavitate, except in an emergency.
During the test dive, some of the hull plating buckles. The pressure hull however is separate from and inside of the outer hull (with water pressure on the latter being equal on both sides of it), so water depth should not affect it in any way.
Capt. Vostrikov refers to the K-19 as the 'flagship'. However, no flag officer (admiral) was present for the duration of its maiden voyage. Furthermore, spending lengthy periods of time under water (and being unable to communicate during those periods) would make a submarine an unsuitable command platform for the Soviet Northern Fleet, of which K-19 was part.
The US Navy helicopter flying around the K-19 is a Sikorsky S-58T, which had its first flight on 19 August 1970, about 9 years after the incident had taken place.
In fact, this is not a Sikorsky S-58T but is a UH-24 which is a variant of the S-58T. The S-58T is the Civilian designator for this bird. Also, the S-58T ended production in 1970. It first entered service in 1954 so therefore COULD have (and actually Would have) been the helicopter used to scout the K-19.
Close-ups on some control consoles show new paint over layers that have been severely chipped, not something one would find on a new boat. However this is based in Soviet Russia it cannot be assumed the submarine/boat is new at all. Also the Soviet Union was known for its lack of equipment and the re-use of materials.
When the submarine has broken through the ice, as well as in the other outdoor scenes, the sun is high in the sky. This close to the North Pole, that indicates that it occurs in summer. However, in the simultaneous scenes from the launching and from the High Command inside Russia, it's snowing, indicating winter. If it was winter, there would be constant darkness where the submarine operated.
In the "fuel fire" on board, the gas jets actually fueling the fire can clearly be seen at the bottom of the frame.
When the second reactor repair team begins welding the new cooling conduit, we spot the maker of the welding clamp: "Uniweld Products Inc" based in Ft. Lauderdale FL - definitely not a USSR supplier.
The white building occupied by the Soviet Navy high command, whose members discuss Captain Vostrikov's intentions, has a sign on the left side of the entrance that says (in Russian) "Cultural Center of the Armed Forces of the Russian Federation in the name of M. V. Frunze". The Russian Federation was created in the aftermath of the dissolution of the Soviet Union. Hence the designation would definitely not appear on any official Soviet building (or anywhere else) prior to the last days of 1991. Michael V. Frunze was a highly respected officer during the Russian Revolution who is still honored in Russia after the fall of the Soviet Union.
Near the end when the men are going onto other sub Liam Neeson's character tells Ford's character all men are accounted for. Earlier in the movie one of the crew abandon the sub. This makes Neeson's statement correct as he does not state that all men are present, only that all are accounted for.
1:27:34 The captain shut off ventilation. On the surface they should be able to ventilate from outside air and open hatches.
As soon as the reactor cooling was repaired they should have lowered all the control rods and stopped the reactor and run one one reactor.
1:27:23 They had red wine to reduce the effects of radiation but did not bring any no iodine.
1:39:16 The fire in aft torpedo room should not have happened. The boat was on the surface for hours. The bucket o fuel should have been dumped overboard.
The film shown by the political officer shows the Civil Rights abuses committed in Birmingham in 1964, four year after the K-19 was launched.
When Radtchenko kisses his girlfriend goodbye he tries to catch what appears to be a Soviet GAZ-66 4x4 utility truck. The production of GAZ-66 did not start until 1966, 5 years after the events of the movie take place.
The Champagne bottle that fails to break when K-19 is christened is labeled (in Russian) as Soviet Sparkling. The trademark "Soviet Sparkling" has not been registered until 1969 when it started selling in the West and was not used internally until 1990s. A bottle made for Russian market would have been labeled as "Soviet Champagne".
When the ship's crew members meet at the end of the movie as older men, Polenin informs Vostrikov that the particular day of this meeting is important. That day marks 28 years since the reactor accident. K-19's reactor accident occurred on July 4th, 1961, but the scene appears to be set in the dead of winter.
At the beginning of the movie, Vostrikov joins naval base by military 3/4 Ton truck. This vehicle is a Dodge WC56 Command Car used by US Army during WW2. Although Soviet troops used a lot of lend-lease US trucks during the War (when both countries were allied), they no longer used it in early 60's.
The sound the camera makes when the group shot of the crew is taken on the ice is that of a fixed shutter, but the camera being used (either a Leica or a Russian copy) would have had a focal-plane shutter.
In the graveyard scene, near the end of the film, the boom mic can be seen reflected in one of the character's hats.
Reactor Officer Vadim Radtchenko says that the accident may trigger a "Thermonuclear" explosion. This is impossible because Thermonuclear explosion is a nuclear Fusion (fusing Hydrogen atoms into Helium and thus releasing energy) and obviously the nuclear reactor in the submarine is based on nuclear Fission (breaking Uranium atoms thus releasing energy).
When the Captain goes into the radioactive reactor room to drag out the last man who was working on the welding, he doesn't close the hatch door to the reactor. This would severely increase the amount of leakage.