The airplane is described as being powered by piston engines; the sounds, the cockpit area, the flight engineer's controls are made to look like a piston engine airplane of that era. Yet, the engine nacelles on the airplane are that of a turbojet or turboprop. That is, a jet engine with a propeller.
In more than one point in the movie, Honey explains the potential failure as being due to nuclear fission of the aluminum atoms, rather than to metal fatigue. In any case, aluminum atoms are not subject to nuclear fission.
Since the late 1930's, airplanes, especially large transports and bombers such as the Boeing B-17 Flying Fortress, had a switch in the landing gear called a "squat switch" or a "weight on wheels" switch to prevent the landing gear from being retracted when on the ground. Additionally, since the plane's engines were not running, there would be little, if any, hydraulic pressure or electrical power to retract the gear - and only one did that.
In reality, it is not possible that a great scientist should not have considered temperature as a variable factor. The fact that you have to have the same temperature when you repeat and compare experiments, is an absolute basic thing in science that you learn already in high school.
Honey tells Scott he is working on a problem in number theory. Honey states that in 1742, Goldsbach postulated that every positive even integer is the sum of two primes. There are two errors with this statement. First, the name is Goldbach. Second, Goldbach's conjecture states that every even integer greater than two can be written as the sum of two primes.
At the end of the picture, Honey recalculates to take into account the test example being in a 'heated shed', whereas at the beginning of the picture, peoples' exhalation vapor is visible while they are talking. There would be no visible vapor in a heated shed.
On the flight to Labrador, the wing outside Honey's window keeps appearing and disappearing.
At Gander Airport in Newfoundland, the pilot refuses to allow Honey back on the plane to continue to Montreal, whilst Miss Corder tells him they'll see him in Montreal, but since Honey was on his way to Labrador, which was part of Newfoundland, to investigate the previous Reindeer crash, he would have been leaving the plane at Gander and not going on to Montreal in the first place.
Perhaps due to Marlene Dietrich's unfamiliarity with UK place names. Teasdale - while in Honey's house - pronounces Farnborough as 'Farborough'.