The scenes set in the days leading up to the onset of the Second World War feature late model Mark XVI Spitfires with 'teardrop' canopies, four-bladed propellers and cannon in the wings. In addition, the serial number on one aircraft (VT151) was an unused number from a block allocated to Gloster for a batch of Meteor F Mk 4's. (The serial can't be V7151 either, as this was an unused number from a block allocated to Gloster for a batch of Hawker Hurricanes - Gloster being part of the Hawker group).
When Bader is demonstrating his ability to fly the Hurricane to his new squadron of Canadian pilots, there is a long cut of the plane flying upside-down in a straight line. This was impossible in the Hurricane, as it had a gravity-fed carburettor. If you look carefully at the clouds, and how the sunlight reflects from them, the image has clearly been inverted.
When Douglas Bader is promoted and sent to command 242 Squadron at Coltishall, the Hurricanes bear the squadron code letters "SD". These were the actual code letters of 501 Squadron which flew Hurricanes in the Battle of Britain. The 242 Squadron codes were in fact "LE".
(at around 2h) The German soldiers capturing wing-commander Bader are shown wearing Waffen SS steel helmets with Wehrmacht uniforms. Their collar patches are Wehrmacht patches while the white shield painted on their steel helmets clearly show the black SS runes.
In the opening scene, raw recruits at Cranwell carry out a short but very complicated drill maneuver in civilian dress. In reality they would have known nothing on that first day.
In fact the "raw recruits" all seem to be ex-Public School boys where they would have been drilled as cadets in school as part of the curriculum, as was common practice until relatively recently.
During the meeting in Dowding's office there is a RAF plaque on his desk with a Queen's crown on it, which was correct for when the film was made, but when as the film is set in 1940 it should have been a King's crown.
When Bader is having a first try at golf he hits the ball after a couple of misses. He says that he hit it only a couple of yards, but the ball can be seen flying off into the distance after a perfect strike.