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.
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.
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.
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.
Continuity mistake: The Avro Triplane goes back and forth between using the authentic four-blade metal-and plywood propeller from the era and a two-blade massive wood propeller. The reason is, the producers originally tried to use the historic designs as much as possible, but had to change some things in the course of the shooting because the originals proved to be not airworthy enough.
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.