When Ms. Matusik has a heart attack, the paddles used to try and revive her are placed in the wrong spots on her chest. One paddle is supposed to be placed on the upper right of the patient and the other on the lower left at the base of the ribs. This allows for proper current travel through the heart. But both paddles are placed on her upper chest at her shoulders. This would do nothing for the patient. Also, you can see the actor jump before she is "shocked."
Blair may be the head of the CIA but he is not in charge of security for the President. That falls solely on the Secret Service for which Blair and Novotny , would have no say in the matter of where the President would be staying.
As Alex is sneaking back into the facility at the loading dock doors, 2 armed Government agents walk by on patrol with a dog (a Doberman Pinscher). Alex hides behind a nearby bush, while the agents and the dog walk past without noticing him. Obviously, the agents are using the dog to foil anyone simply 'hiding' from them, yet the dog does not notice Alex.