During the exchange between the first-class flight attendant and the man who won't turn off his cellular phone, the airline earphones that Reese is wearing change positions multiple times from the right earpiece being on top of his ear, to the headphones being around his neck, to the right earpiece being behind his ear.
In the stock footage for the exterior shots, the type of airliner changes several times.
Reese says he wouldn't risk firing a gun on a plane because hitting a window would depressurise the cabin. This is only true on TV.
In real life, a bullet hole is tiny, has little effect on the integrity of the fuselage, and could be fixed with little effort. A sick bag over the hole would work.
The two supposed Israelis on the plane are speaking Hebrew in a horrible accent and also the female is addressing the male using the wrong pronoun and conjugation. She's talking to him as if he were a female.
The taxi that Holly, the stewardess, enters as she leaves the hotel in Rome, has a red turn indicator. In Italy, like in all European countries, turn indicators are orange.