When Jessica trips the fire alarm, the flashing lights and siren can be seen and heard in the hallway. Once she enters the hotel room, the flashing lights can be seen in the hallway but not in the room. Both would be seen and heard no matter where someone is in the hotel.
Hope's mother refers to Hope as "on athletic scholarship" for track and field at NYU. NYU competes at the division 3 level and therefore cannot give out athletic scholarships as per NCAA rules.
Jessica asks for a "double" but has the bartender pour it in a shot glass. A shot glass is used to measure the size of a single, so it will not hold a double unless the bar is pouring incredibly light shots.
When Jessica answers the phone call from Hope's mother, the phone can be seen from the side, and it still shows the answer and deny call screen.