When Murphy is taxiing the Amphibian out for the first time, he is an absolute novice and does not know how to take off. In making long taxi runs with the aircraft his cockpit is inundated with spray from the river yet in a closeup of Murphy's face, he is bone dry.
The roundels on the aircraft are ones from earlier in the war. The plane appears to be displaying Roundel Type A.1 (or perhaps A.2), which was removed from service by 1942 and replaced with Type C roundels.
The aircraft is a Grumman Duck (J2F-6). None of this type of aircraft was flown by the British or Commonwealth Air Forces during the Second World War. The most common aircraft carried and launched by British sea-going vessels was a Fairey Swordfish.
When charging the dredger towards the submarine and trying to manoeuvre, Murphy hollers "hard to port" then immediately spins the wheel to the right, which is starboard.
The film takes place late in the war and the U-Boat crew is aware when Germany surrenders. Germany had no U-Boats in that part of the Carribean at that stage of the war so Murphy's ship could not have been attacked by a U-Boat.
The U-Boat shown in the film is a post-war American submarine.
When Murphy is flying the plane for the first time, a number of times the plane is upside down. Even though Murphy is not strapped in, he doesn't fall out.
(at around 1h 17 mins) There is modern-day traffic on the far right of the screen crossing a high bridge just above the tree-line.
When the submarine is submerged and stuck on the bank she tries to reverse off and you can hear her diesel engines revving which is impossible as no snorkel was above the surface. Only the electric motors could have been used.