Factual error: When Neo was getting shot outside room 303, Smith fires 10 rounds into him. More if you count every time Neo is shaking in the seat as additional shots. The Desert Eagles in the movie are chambered for .50 AE. You can tell this because the barrel isn't fluted. This means it has a 7 round magazine. Agent Smith runs out of ammo in the subway, so it's not like he can hack his gun because of his software.
Visible crew/equipment: When Neo is crawling round the side of the building after Morpheus's phone call, there are two shots from his point of view. In the second one, close to the black pipe, the square camera is seen in the reflection. (00:15:45)
Continuity mistake: When the agent is running after Trinity, Trinity gets to the end of the roof and runs on. Notice that the end of the roof is red, or a rusty like colour, but when when the agent starts shooting at her, it's turned from red back to probably its original colour of silver. (00:04:15)
Continuity mistake: The subway train that "kills" Agent Smith doesn't pull away from the platform. It simply disappears.
Continuity mistake: As Neo catches Morpheus jumping from the shot out window, Neo holds on to him by his wrist covered by his shirt cuff. In subsequent shots, Neo is shown holding Morpheus' bare wrist, his cuff near his elbow. (01:49:42)
Continuity mistake: After Neo gets shot on the rooftop you see a wound on his right shoulder. However when he was fighting Smith in the subway station, it was gone (seen when he is standing up wiping blood from mouth). Then it comes back when he is running from the agents.
Revealing mistake: When Trinity throws the knife into the guard's face on the rooftop it quivers like rubber when the guy starts to fall. (01:41:35)
Deliberate mistake: When Neo is in the helicopter shooting the agents through the window, watch as one of the agents shoots. He obviously doesn't pull the trigger, because he doesn't move his finger, and there is no recoil, nor a shell ejected. But yet there is a muzzle flash.
Visible crew/equipment: When Smith and the other Agents turn round in the corridor at the end the white reflective screen is visible in Smith's left lens as he is turning. (01:59:40)
Continuity mistake: When Neo steals the guy's mobile phone there is a shot looking back at the man (agent Smith) waving his arm . On the pavement there a few people going both ways. When the close up of Smith happens there are loads of people going left to right and more people on the right side of the screen. (01:54:28)
Visible crew/equipment: When Smith is interrogating Morpheus in the police building, the two Agents come in. When one of them says, "He doesn't know," the white screen is seen in his glasses.
Continuity mistake: At the subway station Smith shoots at Trinity. He destroys the phone receiver and the top half goes flying. But when Neo looks at it, it's hanging down with the top half still attached. (01:49:25)
Continuity mistake: When Neo and Morpheus are inside the hotel room and Morpheus is giving the offer to Neo, the reflection in either part of his shades shows that he is holding his hands away from each other. Yet, when Neo goes to pick up the red pill, they are close together, then we see them further apart from the reflection inside the shades. (00:28:15)
Factual error: In the "Deja Vu" sequence, when Mouse opens the box containing his Auto Shotguns, they are stored with a few belts of .50-caliber BMG ammunition, which would be useless in a shotgun. Also, despite firing about 20 or more 12-gauge shotgun blasts at the SWATs, he fails to hit anyone, even though that equates to about 240 flying lead pellets.
Revealing mistake: After Morpheus and Neo are loaded into the "Jump Program" you can see the Green Screen on the top right corner of the scene. This appears right before Morpheus jumps across to the other building.
Factual error: After securing the rooftop with the helicopter, Trinity calls Tank and says, "I need a pilot program for a B212 helicopter." Tank's screen shows the silhouette of a Bell 206 helicopter. (01:47:25)
Visible crew/equipment: When Neo and Morpheus are in the training program with the girl in the red dress, after Morpheus has paused the program you can see a camera and a black fabric cover around it reflected off Morpheus' sunglasses for a considerable amount of time. Noticeably in the shot considerably close to his face while talking. (00:58:00 - 00:59:00)
Continuity mistake: When Neo is following Morpheus' instruction to escape the agents who have come to arrest him at work, the location of the knot in his tie changes - note the pattern.
Continuity mistake: In the subway fight scene, Neo is thrown to the floor and wipes blood from his mouth on his hand. It then cuts back to Agent Smith. When it cuts back to Neo, he assumes a fighting stance and you can see that there is no blood on either side of his hands.
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.
