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.
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.
Other mistake: The date of birth shown in Neo's passport is 13th September 1971. The date of birth shown in his security file is 11th March 1962.
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.
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.
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.
