When the missile is launched, the Phantom apparently is on the surface, but then in the next exterior shot they are maneuvering underwater with no submerging sequence in between.
While underneath the vessel, the submarine Captain orders the vessel to go to 5 meters below surface. This would have caused the submarine to immediately impact the vessel due to her underwater draft(7-10 meters on average).
There are no pews in a real Russian Orthodox church. People either stand or kneel.
In the Soviet Union, especially in the military, people didn't refer to one another as "sirs" or "gentlemen" but "comrades".
A modern port fully equipped with a substantial number of Gantry Cranes (used for loading/discharging Container vessels) is shown and referred to as a Naval port of 1968 Russia. There would be no use for them in a Naval port.
Bruni says that target is the US fleet at Midway, but there is no major US fleet base at Midway.
The submarine used for filming has been converted to a museum. Stairs inside the submarine used for visitor access are clearly visible. The Soviet "drydock" is also identifiable as the ramp leading up to the side of the ship and not of a style appropriate for a submarine.
The auto carrier vessel shown in the movie is a later model from the 80s and 90s, not available in 1968.
The merchant vessel under which they position the sub is clearly identifiable as an auto carrier in both surface and periscope shots, but the captain identifies it as a tanker.
The B-67 is occasionally called a ship, but any experienced sailor stationed on a submarine would know to call it a boat.
During the film, characters refer to a pursuing Soviet submarine as a "November". The Soviets' first class of nuclear submarines were officially known as Project 627. The code name "November" is a NATO designation, and would not have been used by Soviet personnel to refer to their own boat.