When Dana is being escorted to the elevator in the East European Trade Center, the floor leading to the elevator is continuous revealing that it is not a real elevator as it would be unable to move.
Dr. Tabor surgically implants a device in Paris' brain in a medical room where no one is wearing masks, gloves or any other operating room equipment -- two guys are in their business suits -- and Paris is not on anesthesia or breathing equipment.
Barney uses a rifle scope to aim while shooting a grappling hook on a rooftop. A scope would serve no purpose in this situation -- there would be nothing to aim at.