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.
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.