Revealing mistake: When the men are waiting at the dock and when boarding the submarine, we see the wide shot of the submarine and the dock. The ocean is, however, incredibly calm despite there being torrential rain happening throughout the scene on the dock. While it's not seen, this would be from a rain machine not able to cover the entire location of the shot. (00:13:51 - 00:16:38)
Revealing mistake: After the XO orders all stop, we see a close-up of the ship's yoke being pulled back. The next wide shot shows the interior as the bow of the sub is rising, and just before this shot ends, note the console that the man with headphones is working at. A pair of crewmembers cross paths in the foreground, then the entire console wobbles, proving it isn't attached to the floor at all. (01:09:00)






Answer: In a war situation, the Captain is absolutely NOT allowed to try and contact anyone, lest it gives their position away, which is why he was unable to question or confirm the order.
GalahadFairlight
All respect to GalahadFairlight, but Hunter was not asking the Captain to 'contact' anyone, but rather to use all possible measures to receive the EAM. Active contact was not required, and in fact, going shallow would have been 100% necessary just to launch the missiles, at which point VLF reception would have been easily possible. No nuclear submarine captain would ever have been so stubborn, nor so dismissive of his own XO. Both of these were pure Hollywood inventions.