Continuity mistake: When Neo is in the helicopter firing the automatic weapon into the building he is moving the gun horizontally. The bullets strike vertically, though, starting from the floor near the window and traveling upwards towards the back wall of the room. There are two shots that show this.
Continuity mistake: In the scene right after Neo steals a man's cellular phone, we see him running down an alley with the back of his shirt untucked from his pants. After cutting back from the agent who's chasing him, we see that Neo's shirt has miraculously tucked itself back into his pants.
Continuity mistake: When the guard asks Neo to remove any metallic items after he sets off the metal detector, Neo's coat is open, and he's just got a T-shirt on, with no guns strapped to him. In the closeup, all the guns are visible. Most are down the side, but we should have seen the pistols in his belt from the earlier angle. If nothing else, with his coat open as much as it was, the guard should have spotted the weapons even before he opened it further... (01:37:00)
Continuity mistake: When Tank comes into Neo's room and talks to him, just before his training, note that there is a rip in Tank's shirt near his right shoulder. Near the end of the scene, the shot changes to Neo, then when it cuts back to Tank, there's no rip. When it cuts to Neo and back to Tank again, the rip is there.
Continuity mistake: Near the end of the movie after agent Smith shoots Neo. Trinity is whispering to Neo, as she leans toward him there is a small strand of hair on Trinity's right temple slowly falling down on her face. The shot changes to Neo's face and back to Trinity where her hair is now perfectly in place and the strand is gone.
Continuity mistake: In the beginning of the movie, where Trinity runs from the agents, she jumps towards a window. She turns slowly in the air, eventually facing upwards when she crashes through the window, no longer turning. From the inside shot, however, she comes through it face down (so she can roll forwards down the stairs). (00:04:55)
Continuity mistake: When Cipher is making the deal, one second he is holding his cigar in his right hand, then all of a sudden it is in his left. (01:02:25)
Continuity mistake: When Morpheus and Neo are fighting in the training simulation, just after Morpheus says, "You think that's air you're breathing now?" there is a pause before he prompts Neo, "Again." The shot goes to others watching on the monitors, notice Dozer looks to his left in the direction of Mouse. In the next shot the camera cuts to Cypher and Trinity (who are sitting behind Mouse) but Dozer's head is now facing the opposite direction it should be. (00:50:10)
Continuity mistake: When Trinity and Neo have rescued Morpheus and are flying through the air, Neo drops Morpheus then Neo lands, but Neo is halfway on the rooftop, yet when he grabs hold of the rope and is dragged along the rooftop, he is sliding almost the entire length of the rooftop. (01:46:05)
Revealing mistake: When Agent Smith is fighting with Neo in the subway, Neo's back is against a pillar. The area of the pillar which Agent Smith punches away with the first punch is visible before Neo ducks, and then he punches it away. You have to look carefully, because it only appears for a very short period of time. (01:50:35)
Other mistake: In the bullet-time sequence in the subway station the lighting on Neo and Agent Smith doesn't change even as they spin round each other, principally because they were in a green screen chamber with even lighting to shoot the movie. It sticks out because the lighting on the CGI set (for the bullet-time shot) is pretty dim with light in specific areas. (01:50:10)