At the start of the episode Hasim Farouk is seen shooting his handgun at a van firing around 14-15 rounds without changing the guns magazine. Later Detective Esposito identifies the gun used as a Sig Sauer P220S. A sig Sauer P220S has a maximum capacity of 8 rounds in the magazine and 1 in the barrel for a total of 9 rounds. Since no magazine was changed during the shooting there is no way for a Sig Sauer P220S to fire the 14-15 rounds.
When Gates called Backett and Castle out of the room to introduce FBI Agent Harris, Castle tried to close the door but it didn't shut. After they introduced to each other, Agent Harris open the door to enter the room.
When Castle realizes Alexis was also attending the lecture with Sara Al-masri (the missing girl) and calls her phone, you can see the phone is in Airplane mode but still ringing.
On the roof, Alexis screams before the abductor grabs her from behind where she could not have possibly seen him.
The communications room in Paris, France has US style light switches on the wall, and the corridor has US style PA speakers and fire alarm annunciators on the wall.