Russian Submarines (or others) do not have short wave radio reception or transmission equipment arbitrarily switched on. It can easily be detected.
In the Pentagon scenes, the United States Flag is hanging backward. The blue "union" should be in the top LEFT corner.
Evading a second pair of American torpedoes, Captain Gregoravitch orders the crew to deploy countermeasures and make a hard turn to "starboard" (right turn). The exterior visual shows the submarine turning left.
Methane does not "burn" in 80 miles altitude (almost vacuum, partial pressure of oxygen is completely insufficient).
The Ozone layer does not shelter from CMEs, it absorbs UV radiation, which is quite unrelated.
A caption describes the setting of an early scene as "The Pentagon, Washington, D.C.". Though the Pentagon's technical location is actually in Arlington, Virginia. However, it has been insisted that the building is not just close physically, but is very linked to Washington's political and economic culture, that the employees generally think of themselves more as 'Washingtonian' than 'Virginian'.
The admiral is not wearing a U.S. Navy uniform. The dress blue uniform does not include shoulder straps with rank on them.
When Lucas Foster flies off in the plane on his way to the Russian sub the Canadian flag is visible on the tail of the plane.
At the end of the film, Lucas walks down a gangplank from a "US" Destroyer, to have lunch with the US President. However, US warships are gray in color with their ID numbers painted on the bow. Australian, British, New Zealand and other "British" Commonwealth Warships are an off-green color with the numbers painted amidships. Also, those ships are WW2 style reserve vessels - far from being "current".
The same character who breaks a news story as the studio-bound anchor of a supposed major news network early in the movie shows up a few scenes later as a scrum reporter with a hand-held recorder. Though not impossible, it is highly unlikely that a high-profile professional journalist would fill both roles.
Officers in the U.S. Navy do not wear their covers (hats) indoors.
When Joanna Parks was giving geographical coordinates to Lucas Foster, she pronounced "Longitude" with a hard "G" sound rather than a soft "G" sound.