Plot hole: In the movie the German sub is in the middle of the Atlantic about 1500 miles from the American coast the American submarine is an S-Class boat which had a top speed on the surface of 12 Knots even less underwater and it spent part of the trip submerged. This means that it would have taken them at least 5 or 6 days to reach the German Sub. This is 1942 There would have been dozens of other German subs a lot closer who could have come to their rescue.
Plot hole: The Americans disguise S-33 as a German Type VII U-boat to pose as the German resupply boat. This is a pretty bad idea, since all resupply boats are of the Type IXV and not Type VII. Of course in a severe storm the differences between types might go unnoticed, but the plan could not rely on that alone. In good visibility, any able German watchman would be able to spot the difference quickly.
Plot hole: At the beginning of the movie, the German commander sends a radio transmission with the damaged sub's position at "AL 85-32." The German Kriegsmarine divided up the Atlantic in grid squares like these, but "AL 85-32" means the damaged sub is just roughly 375 miles west of Ireland, but more than 2700 miles from the US east coast. There is no way on earth the Americans beat the Germans to this location, especially since the German supply sub is already en route. Funny enough considering the controversy about the movie, for this position the British would have been in perfect position to intercept.