Factual error: Terry-Thomas's plane gets stuck between the carriages of a Paris-bound train (in fact filmed on the single-line track between Bedford and Hitchin). Just before the train plus plane goes into a tunnel you can see the cooling towers of Bedford's Goldington Power Station (circa 1960) behind TT's head.
Continuity mistake: When the German colonel crash lands in the Canal, he first hangs directly under his upside-down plane before he has to let go, and the plane zooms in a straight line away from him. But as he resurfaces in the foreground, the plane comes in from the background's left before landing in the water.
Factual error: The British pilot takes off in his Avro Triplane even though the American pilot hangs from his tail. By our modern standards, the planes of this era would be considered ultralights. The weight of a human hanging from its tail would put any ultralight so badly out of trim that it would stall instantly, even assuming it could handle the extra weight of a second person at all.
Other mistake: The Japanese plane and the German plane are actually the same aircraft, a British Design called an "Eardly Billing". The "Japanese" version is re-dressed with canvas partitions between the wings, painted dragons, etc, the "German" has no canvas and German eagles, but they are the same machine.
Continuity mistake: The number of tail fins on the "American" aircraft changes from two to three depending on the shot.
Continuity mistake: In some scenes the "Antoinette" flown by the British flyer has authentic, thin "wing warping" wings. In other scenes it has thick modern glider wings with ailerons. This was done because the authentic machine wasn't very airworthy and was modified during the shooting.
Revealing mistake: When the tail breaks off of the "German" machine and it careens around the field, you can see the little steerable tail wheel used to control the plane in those scenes. In all other scenes this plane has a tail skid.
Continuity mistake: When Sir Percy attempts to spy the other fliers from the hangar roof, he uses a ladder to get to the top. But when Dubois startles him and he slides off the roof, the ladder on the roof slope is gone.
Plot hole: Before the race starts, Sir Percy intends to sabotage some of the other fliers. He announces to Courtney that he had lured Dubois away by giving him the address of Courtney's daughter, but later, when the race starts, there is nothing wrong with Dubois' machine even though Sir Percy had the chance.
Other mistake: As the planes go over Dover you get a very nice view of the modern harbour complete with cross Channel ferries and oil tanker.