Throughout the film, the airliner depicted is a Douglas DC-6 or DC-7, but in the shots of the airplane hitting the water, the miniature used is a Lockheed Constitution - a double-deck transport of which only two were built for the U.S. Navy.
When they lose the first engine they are at cruise speed. The captain feathers the prop and calls for flaps. Flaps at that time are the last thing you would use. You are going too fast to safely lower them and you would not want to add the extra drag caused by full flap extension.
The pilots state several times that the #1 engine is feathered. In the exterior shots of the plane, which appears to be a model, the prop is not turning and you can see the blades. They are not feathered. Feather props are turned to present only the edge of the blade to the wind to minimize drag. The props on the model are in normal power mode and when not rotating would create a lot of drag.
In the exterior shots, the airplane is actually a DC-6, The DC-7 had four-bladed props with spinners. As incorrectly mentioned above, the airplane is not a DC-4--the DC-4 had oval cabin windows.
Although not stated in the film, the filmmakers clearly intended to depict a Douglas DC-7C. In the exterior scenes we see the "7 Seas" logo on the vertical fin, and in the close-up scenes of the engines we see four-blade props and prop spinners, as on a DC-7. However, with the exception of the logo, the plane shown in the exterior scenes is a DC-4, evident by the more rounded shape of the vertical fin, the length of the aircraft and no prop spinners.
The information above is incorrect. Both outboard engines have failed, the were able to feather the left (#1) engine which keeps the prop from rotating and creating drag. They failed at an attempt to feather the right (#4) engine so it continued to spin from the airflow which creates additional drag and thus needed extra fuel to make their destination. This is the reason they were forced to ditch.
At 16:13 in a scene set in Lisbon, Portugal, a Western Airlines DC-6B is seen taxiing in the background. Western Airlines did not fly to Portugal in 1958.