The Capt is wearing his red hat. That's only used in drills when he's an observer. It indicates that for the purpose of the drill, he's not really there. Also, at the time ICBM's used solid fuel, there was no need to "fuel" them. The EAM the Capt reads is also not the same EAM they first received. Also rank indications are incorrect on like...90% of the people in that scene.
I love that movie, I've watched it a dozen times at least, twice with submariners from the US Navy. Man they nitpick.