+1 for the Crimson Tide reference!
After talking with nuke submariners about generalities, the last I heard about a nuclear launch off a Trident was close as the movie portrayed. However, the end credits claimed protocol had been changed to only the President to authorize a nuclear launch.
I and they laughed at that because it has always been so. No captain of a Trident has ever had unilateral authority to launch nuclear weapons. Still, a good movie. Not sure if the lack of comms (partial flash messages) could create such an incident. I tend to believe that we have so many fail-safes, as not to start a nuclear war.
I sleep well at night knowing those Sailors are manning the tubes on our Tridents. Bombers can be blown out of the sky; ICBM's can be intercepted (if we have any left), but the Tridents are patrolling everywhere, and know one knows where they are. THAT is what keeps the world balanced. God bless, our Trident submariners.