They show a sailor on the sub fall off into the water. No one moves. Later they show the body floating in the water. That would never happen. As soon as he hit the water, man over board would be called and someone would have jumped in after him to save him. There would never have been time for his body to just be floating in the water. They would have immediately recovered him and attempted life saving procedures.
JD states he drove in with a "Kia" and that Mackey came in on an "Aircraft Carrier". The Ship Mackey came in on is not an aircraft carrier. In fact, it is not even a US Navy Ship. It's the HMAS Choules of the Royal Australian Navy.
Radium isn't the nuclear fuel used on nuclear submarines, in fact it's not used as nuclear fuel at all. The actual fuel is uranium.