In several scenes in the movie, a German Messerschmitt Bf109 is seen entering into a dive, trying to shake a Hurricane on its tail. The Hurricane dives after the 109, catches up with it, and shoots it down. This is somewhat implausible, since the 109 was much faster than the Hurricane (and the Spitfire) in a dive - diving was pretty much a sure-fire way to escape a British fighter.
Far from being the undisciplined rabble that is depicted in the film, the Polish pilots were known to be polite and elegant, and generally of a better breed than most of their English counterparts.
Some pilots refer to Eva Braun, implying that they knew about her relationship with Hitler. That relationship was a secret, and wasn't known even to the Germans until after the war.
The squadron's first victory, while still in training, is a Dornier Do-17 bomber (identifible by its twin engines, glazed nose, and twin tails). While it was first identified as such, it was later known it was a Messerschmitt Bf 110 when the remains of the plane were excavated in the 1980's.
When the Czech pilot gets on the bus after his altercation with the other airmen, he tells the Poles that he speaks Polish. Polish and Czech are often mutually intelligible, and both Poles and Czechs would have known this.
As Frantisek makes his wheels-up landing we can see that the propeller is turning throughout the landing. Yet when he comes to a stop there's no visible damage to his propeller.
At about 1:28, the code letter "R" on Zumbach's Hurricane is loose at the edge, as it is a sticker and not painted on as it would be in real life.
In the final scene at the hotel, the Union flag can be seen on the pole outside the window. Sadly, this flag is being flown upside down as the broad white stripe is at the bottom of the pole and not the top.
The shoulder eagles on Georgina's uniform are the wrong way around. The eagles should face the wearer's rear.
Early in the movie, one of the women mention her nylon stockings. They had just become commercially available in the US, and had yet to be introduced in Britain.
In one of the first scenes set in 1940, a German half-track appears, bearing the trident symbol of the 2nd Panzer Division. That symbol was first introduced in 1944.
Jan Zumbach had Swiss nationality and did not have to return to Poland at the end of the war. He would surely have mentioned this. And did not in fact leave, and later served as a mercenary in African wars.