Continuity mistake: When Alex wakes up and goes to sit next to Tom, she puts her right arm around him so that her hand is hanging over his shoulder. In the next shot, her hand isn't visible even though his shoulder is and his hands are down. In the next shot, her hand is back on his shoulder and he's holding her hand.
Continuity mistake: When we get the shot of the President sitting and holding his glasses, the glasses change position in the next shot. When his back is to the camera, he's holding them so his thumb is in between the lenses and the earpieces are facing to his left. When he's facing the camera, the glasses are flipped over so that the earpieces are facing his right.