Visible crew/equipment: In the highway sequence, when Trinity hard-brakes the bike and stops to make a burnout U-turn, we can see the cam attached to the right side of the bike. In the same scene we can see that the headlights are off but Ducatis designated for the U.S. market don't have a switch to turn off the lights; once the ignition is switched on the lights are automatically on as well.
Continuity mistake: Right before the car chase when the car exits the garage the parking lights are on. Then it makes a right turn and one of the parking lights is out (The one on the passenger side). The next time you see the front of the car both lights are on.
Continuity mistake: Right at the beginning of the fight between Morpheus and the Agent on top of the semi-truck, the Agent sends Morpheus sliding to the side of the trailor. In the first shot, Morpheus' left leg is over the edge, but in the next shot, his whole body is on the trailor and he has to turn to get close to the side.
Continuity mistake: In the burly brawl, Neo gets tossed into a brick wall and gets dirt and concrete dust on his back. When he lands on the ground his back is suddenly clean.
Continuity mistake: In the corridor of many doors where Neo fights all the Smiths the two furthest Smiths draw their guns twice.
Visible crew/equipment: In the freeway chase, there's a black Oldsmobile Alero that flips just beside Trinity's Caddy. If you play it slowly (not essential, but helps), you can briefly see the rust coloured ramp used to flip the Alero.
Continuity mistake: When Neo is fighting the three agents, the glass of the streetlamp falls. When he flies off, the glass on the ground disappears. In the next shot, it reappears when the Agent Smiths are walking on it.
Continuity mistake: When the Merovingian's henchmen are shooting at Neo, a shot is shown from the side to show everyone firing their weapons. The man on the far left (the closest) makes the arm movements to indicate that his weapon is firing continuously, but his gun is only seen firing once.
Continuity mistake: In the car chase scene, just before they go onto the freeway, the twins fire a machine gun at them and make quite prominent dents on the top of the car. However, in the scenes that follow, the bullet holes are not there. This is most obvious when you see the car from the top and the black car next to it crashes into a barrier. They come back when an agent lands on the top of the car and rips it off.
Continuity mistake: Right before the Twin enters Trinity's car, he shoots a black car in front of them and then continues firing on Trinity and Morpheus. However, when the car is seen flipping in slow-motion, you can see bullets hit on the hood of Trinity's car up to the windshield and then instantaneously go to the roof.
Continuity mistake: The tire on the front wheel of Trinity's Ducati 996 changes from slick to treaded a couple of times between shots.
Revealing mistake: After the twins shoot the black Oldsmobile, it hits a barrier and does a spiral, and lands on its roof. That's impossible because the car's fender would have been torn off. It would have skidded a sharp right and went under the semi that Trinity was driving by. That indicates that there was a ramp to lift the car off the ground and do the spiral.
Deliberate mistake: In the scene where Neo is sitting with the oracle and talking, there is one quick shot of the fence area where Smith comes in. In spraypaint on the metal fence it has "ONE" written across it diagonally up to the right. When the oracle leaves and Agent Smith comes through the fence entrance the spraypainted "ONE" has disappeared.
Continuity mistake: In the scene where Neo meets the Oracle, when Neo and Seraph are in the corridor with all the back doors, the small piece of wall around the door is white. However, when Seraph opens the door so that he and the Oracle can go through it, the borders of the door opposite to the open one are green.
Continuity mistake: The door which is held open by one of the Twins gets splattered with blood on the inside when Trinity shoots at his arm. However, when Neo later runs towards the door before bashing it in, the splatter is gone.
Revealing mistake: When the Keymaker closes the door with the Smiths firing at him, if you play it slowly you can see that no bullets actually hit him, as they would have caused bullet holes and blood stains, but his shirt stays perfectly fine right up to when he shuts the door.
Continuity mistake: When the 2 cops are being morphed into at the beginning of the highway scene, the driver is looking to his right while being morphed, but in the immediate shot, he is looking to his left, there isn't enough time in between shots for him to look the other way.
Continuity mistake: When the Tahoe is getting hit and crashed it loses its passenger mirror. When the Tahoe is hit by the other drivers the mirror is back on.
Continuity mistake: In the scene right before the freeway scene, in the city streets, the Escalade EXT rams a brown BMW 7-series in the purwuit of the Silver CTS. The BMW rips in half, but there's not a scratch on the EXT. Later in the freeway scene, you see a headlight blown out, and a katana sword can rip it, whereas a car smash causes no damage.
Factual error: In the freeway chase, when the agent tears off the car roof, it is seen as a floppy metal sheet. A roof is actually quite thick, supporting part of the car's structure, a built-in roll-cage, and of course the headlining. However, all of these things are nowhere to be seen.
Answer: This was made just for the trailers. The same part (without the Matrix code) can be seen when Smith says "suprised to see me?" to which Neo replies "No." and puts on his sunglasses before the Burly Brawl.