Continuity mistake: In the "Deja vu" scene, Neo uses a CZ99 pistol to shoot through the wall at the police officer, but when Agent Smith bursts through the wall and grabs him, Neo is holding a Glock 17.
Other mistake: They are presumably in the US - trying to make it look that way, anyway. Cars driving on the right, speaking English etc. However the filming location was overseas, revealed by the elevator in the lobby scene. When they hit the button, the plate refers to the elevator as a lift.
Suggested correction: As pointed out in several other mistakes, The Matrix is a computer simulation and is not meant to be a perfect model of the world. Small things like this are possible.
Revealing mistake: In the scene when Trinity makes it back, after Morpheus is taken, she hugs Tank. When she hugs him, you can see that she doesn't have a jack in the back of her head.
Suggested correction: In fact, she has the plug.
Continuity mistake: In the subway fight sequence between Neo and Smith, you see Smith swing his right fist toward Neo. When the camera cuts to a closer shot, Smith is swinging his left fist toward Neo.
Other mistake: In the scene where Cypher is sitting on Morpheus right after betraying him, Morpheus is still plugged into the Matrix. Yet he can be seen blinking just before the scene cuts away. It can be seen when the camera cuts to behind his head.
Revealing mistake: When Neo stops the bullets being shot at him in mid air and they fall, you can see that there are not grooves in the bullets. As a bullet passes through a barrel, it picks up the impressions of the lands and grooves of the barrel. Since the Matrix is a simulation of our world, including the involved physics, the lack of rifling grooves is an oversight by the special effects team.
