When Captain Courtney is rescued, he jumps on the wing and hangs onto the strut. When the actual aircraft takes off, not only was dummy used much further forward on the wing than Captain Courtney was, but it is an entirely different plane - a two seat trainer.
Almost all the flying aircraft that don't crash are the Travel Air 4000, which was produced in USA from 1926 to 1929, so could not have been in use in WW1. It was produced for private flying and was never a military aircraft.
Many of the aircraft seen on the ground are the Nieuport 28 - which was a WW1 fighter, but was French (and was not flown by the British) and did not fly until 1917 (the film is set in 1915).
When Courtney is signaling Scott before attacking the German base, you can see the plane in the background superimposed on all the foreground elements, including Courtney.
William Janney's character name is credited as "Gordon" on screen, but he is called "Donny" throughout.