Continuity mistake: In the scene of the freeway chase, where Trinity, Morpheus and the Keymaker are in one car on the right side of the freeway, there's a shot from the car of the Twins (two or three lanes to the left), Trinity's car passes a truck, when the car appears again ahead of the truck there is only the driver inside the car, no passengers.
Revealing mistake: After Neo takes the pole for the fight with the Smiths, we have some "bullet-time" shots of Neo fighting with the pole. In those shots we can see that Neo and the pole are computer made. This becomes even more obvious because before using the pole Neo was crushed into a wall and got all dirty and the computer-made Neo is completely clean.
Visible crew/equipment: In the car chase when one of the cars flip forward toward you, (looking back down the freeway) for a split second there is a sideways view of the car and you can see a black box type shaped object with cables in the drivers area, but no driver - guess the flipping ram equip. This mistake can be seen on the UK DVD.
Continuity mistake: In the scene when Neo and the counsellor Hamann are holding a conversation at night before entering the engineering level, you can see Hamman's robe's neck changing from wrinkled to unwrinkled mainly on the back side between shots.
Revealing mistake: One more of the Burly Brawl. After Neo is thrown over the park chair and this is broken, count five shots starting with the close up of Neo face, you will see in the end of the fifth one, how an agent loses his wig.
Factual error: This happens throughout the entire film. Whenever bullet hits are shown on objects like cars or walls, the hits always appear to have been made from a weapon fired directly at the object - no matter what angle the shooter is actually firing from. This is particularly noticeable in the highway scenes. Bullet hits make very different impact scars/holes depending on the object and the angle.
Revealing mistake: In the office building, when Trinity runs and jumps out the window, she seems to pull the Uzis out of nowhere. She is wearing a skintight leather jumpsuit, and previous shots show her not holding anything and with nothing attached to her.
Continuity mistake: In the fight scene between Seraph and Neo, items on the tables are constantly being knocked off and reappearing. In the first long shot, where Seraph and Neo jump from the rightmost table to the one adjacent, a bottle is knocked off, and then reappears. Almost immediately after, during an overhead shot, Seraph knocks one of the flat ashtray-like containers off the table. He moves back, obscuring the place where it was. When he moves forward again, it's back on the table.
Continuity mistake: DVD: In the 100 Smiths brawl, Neo dives backwards about four feet from the ground and a Smith dives at him from the ground to Neo's left. The following shot shows both of them at about twenty feet in the air and it looks like they are descending from the fourth floor of the building in the background.
Continuity mistake: After one of the agents rips the roof off the car on the expressway, there are some shots that show the interior of the vehicle still dark as if the roof were still intact.
Continuity mistake: In the scene where Link unplugs Morpheus from the Matrix there is a close-up of Link with Morpheus opening his eyes at the bottom of the screen. In the following two shot, Morpheus still has his eyes closed and opens them up moments after he had already has awakened.
Visible crew/equipment: After the agent crushes the Oldsmobile, look inside and you'll see air cannons and a roll cage.
Continuity mistake: During the freeway scene, the Twin shoots a black car directly in front of Trinity's car. He shoots on the hood and then a trail of holes are seen going up the windshield. The next shot is one from inside Trinity's car between Trinity and Morpheus, but no bullet holes are in the car ahead.
Continuity mistake: During the freeway chase, when the car is crushed by the agent, look closely and you'll see a white Monte Carlo land on top of a mini-van. About 30 seconds later you see the same thing, but up close.
Continuity mistake: In the car chase during a few scenes, the number plates on the truck, Trinity's car and the police cars seem to have no registration numbers.
Continuity mistake: When the Keymaker opens the door inside the white corridor near the end, you see in the reflection on the doorknob and it shows the corridor, but it does not have any doors in the reflection and there is a white door behind the Keymaker, which you cannot see otherwise when you look in that direction.
Revealing mistake: In the highway chase scene, Trinity, Morpheus, and the Keymaker pull off onto an exit and the twins follow. If you look closely at the exit and the overpass, you can see that it ends after it goes over the highway. The exit/overpass goes nowhere. You can see this during the various shots when Morpheus faces off against the twins and later when Trinity looks back at the overpass from on top of the Ducati carrier.
Continuity mistake: When the operator on the Vigilant is impaled, at first the bar seems to be coming out of his chest horizontally. When they show him again later as the ship explodes it seems to be pointing much higher up.
Continuity mistake: When Neo is fighting the three agents at the beginning of the film, the ground is really dirty but when he flies off, there's only some papers and the ground is dirty again after that.
Continuity mistake: In the scene where Trinity is driving on the freeway, you can see from the interior shot that her door is locked. In the exterior shot you can see her door is unlocked. This is consistent all the way through the driving sequence.
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.