While inside the creature the diving party is not wearing or holding their flippers, but when they emerge they are wearing them again.
Shortly before the collision, Captain Crane orders Seaview rigged for silent running, and orders are given for no unnecessary movement on board. Yet throughout the remainder of the scene the SONAR system continues pinging loudly. As SONAR works by sending a sound pulse out into the water to be reflected back to the sub by objects, they might as well be pounding on a gong for all the good "silent running" is doing.