Darius plays an LP record on a Victrola. He should know an LP record plays at 33 1/3 rpm and Victrola plays at 78 rpm. LP would sound like a chipmunk and would ruin LP.
Defense officials from different countries do not conduct diplomacy. The Secretary of State for the US, under direction of the President would reach out to Russia, even if the ice had been broken by actors as was depicted. The role of the Pentagon would be to say "yes sir" to the President, not Russian officials.
Three Russian submarines are off the coast of Florida, and the audience is told that these submarines will shoot down a rocket launching from Kennedy Space Center... Submarines have almost no anti-air capability. To detect a rocket launch from 200 miles would require a very advanced air-search radar, and a missile capable of hitting such a rocket would have to be very advanced. The Russians have some land-based ABM systems, but no ABM systems deployed in their fleet.
And an ABM system on a submarine is one of those "only in Hollywood" ideas.