Both the German and British troops fighting to recover the Baron are armed with British SMLE's. The Germans should have been using Gewehr 98's. The notable difference being the SMLE has a protruding box magazine.
In the second dogfight scene (about 14 minutes into the movie) a radio antenna is visible behind the pilot of a German fighter. WWI airplanes would not have had radios (if there where in fact any, the close-ups of the airplanes on the ground show no antennas).
When Von Richthofen's DR1 is landing the last time after he is shot by Brown, it is obvious the engine is a radial and the propeller is a Sensenich Metal prop. The DR1 used an Oberursel Ur.II rotary engine and a wooden propeller.
There are many scenes in the film where the sunlight is not correct. Often the planes are seen fighting on completely overcast days, when suddenly there is a few seconds where the sky is blue in every direction and the sun is shining on the pilot or plane. In one scene on the ground, several pilots are discussing the death of one of their peers. They are in the shade of a wing, then standing in the sun without moving.
Hermann Goering was not assigned to the Flying Circus until he took over as its commander several months after Manfred von Richthofen's death. Also, his later reputation notwithstanding, there is no evidence that Goering ever machine-gunned civilians or committed other atrocities as a World War One fighter pilot.
The national anthem, you can hear during the German empire scenes, is the republican anthem, introduced after the revolution 1918. Funny enough the German anthem during the Kaiserreich had same melody like UK anthem 'God Save the King'.
The German ace Oswald Boelcke was not killed when his plane collided with Von Richthofen's plane. Instead, Boelcke was killed when the undercarriage of Erwin Böhme's plane crashed into his plane, causing the upper wing to fall away. Böhme's plane survived the mid-air collision and Böhme later became an ace himself.
Use of an "interrupter gear" cam mechanism to allow fuselage-mounted machine guns to fire through propellers without shooting them off by stopping the gun whenever the propeller was in the way caused a far slower rate of fire than shown in the film. (The British SE-5 simply avoided the problem by mounting a machine gun to the plane's upper wing and firing over the top of the propeller.)
In the film, Von Richthofen was shot and wounded on the skull while fighting against British single-seater scouts. In fact, on July 6, 1917, he was shot on the skull and seriously wounded by a bullet fired by the observer's gun of a British F.E. 2 two-seater.
In the film, on the day of his death, Von Richthofen was seen flying a Fokker Dr.I with Maltese Crosses (with curved edges) painted on it. In fact, at that time the Maltese Cross had been replaced by the Balkan Cross (with straight edges) as the national emblem on German planes.
When Von Richthofen is playing billiards with the other members of the squadron, half of the shots he "makes" are scratches, where the white cue ball goes into the pocket, rather than any of the balls he's shooting at. Normally, when a player scratches the cue ball into the pocket, shooting goes back to the other player.
In the final dogfight, when Brown kills Richtofen, first Richtofen is chasing Brown down a river, then suddenly Richtofen turns around and runs back the way he came, allowing Brown to turn back and follow and kill him. This is impossible, no flying ace would just do a U-turn while pursuing an enemy and allow the enemy to gain the advantage like that.