At 1hr 45min and 7sec during the helicopter shoot - em - up scene, notice the aluminum chair on the left. It starts out facing the desk and moves to different positions throughout the scene. At one point, it is facing the desk again and then it faces Morpheus. Then, it is knocked down and magically goes back to its original position. Immediately after, it gets shot back down. This chair seems to have a life of its own!