Deliberate mistake: The French NATO rescue team is flying an old, Russian-made Mi-17 helicopter which is not in service in France. It was probably rented in Slovakia where most of the film was shot. The Mi-17 is easily distinguished from the French multi-purpose helicopter Puma: the Mi-17's landing gear is supported by huge rods, its side windows are round, and it has a sleek boom with the tail rotor on the left side. The Puma has smaller gear support, rectangular side windows, and a thicker boom with the tail rotor on the right side. (01:15:42)
Deliberate mistake: The aft cockpit of the F/A-18F is not simply a 'Navigator' as they say several times in the movie. It is the Weapons Systems Operator, or WSO (Wizzo).
Answer: Totally impossible. You can throw a lit cigarette into a pool of jet fuel and it won't ignite.
stiiggy