Being pitched out of the helicopter to get on a U.S. Navy vessel is based on the original 'Hunt for Red October' novel.
The Headset, that the Navigation Officer on the "Fearless" wears is a Logitech G PRO X, which is a gaming headset.
Captain Andrew Bennett is wearing US Navy Commander insignia and his name badge says CDR. The commanding officer of a ship is referred to as "Captain" regardless of rank. This happens a second time in the final scene on board the Russian ship.