At the beginning of the freeway chase, after they come out of the parking garage, Trinity and Morpheus' car goes around a left turn. We then see the action from the twins' point of view, and during one shot the heroes' car is obviously stationary, parked diagonally against the sidewalk. It must be the heroes' car because no other car of that model is seen in the scene.
In the Freeway Chase, Morpheus stabs a sword into the side of the truck that he is standing on as he approaches Trinity and The Keymaker. In order to snatch The Keymaker from Trinity's bike, he placed it low down - near the wheels and stood on the hilt. Later on in the scene, when he's fighting agent Thompson he is struck to the ground, near the edge of the truck roof. He spots the sword which is now mere inches from the roof - close enough for him to grab while remaining hunched over the edge, which certainly would not have been possible in its previous location. Furthermore in the scenes leading up to this, the sword has vanished from the side of the truck, most noticeable when the camera pans around the entire vehicle.
During the chase scene on the highway numerous cars are crashed and/or destroyed in the center of the highway and a large amount of wrecks litter the road so all traffic should have stopped and been completely backed up at that point, however as they start forward on the motorcycle, and subsequently backwards when they turn to avoid the agents, traffic is still flowing normally, like no wrecks had happened.
At the beginning of the fight in the Merovingian's foyer, Neo stops his attackers' bullets and they fall to the floor. The fallen bullets disappear and reappear frequently throughout the sequence, most notably vanishing in the overhead shot (when Neo kicks the ponytailed man through the railing), but reappear moments later on the ground.
In the Nebudchanezzar, Link unplugs Morpheus from the Matrix. In the close-up we see Morpheus opening his eyes in the bottom of the screen. When we cut back to the two-shot, Morpheus still has his eyes closed and opens them up quite deliberately moments later.
In the highway chase scene, Trinity and The Keymaker jump onto a truck with motorcycles. When shot from above, Trinity holds The Keymaker in her right hand, but in the next shot which is shot from below the bridge, the Keymaker is behind her slightly to her left.
When Neo first meets Seraph and they duel, they jump onto a table, and a container of chopsticks sitting on the table is knocked off the edge. A few seconds later, they jump to an adjacent table, but the container has reappeared in its original location on the first table, upright and with the chopsticks still inside.
In the tunnel scene to the freeway, the human police officers are driving a Chevrolet Caprice made prior to the 1994 model, from the next scenes, it appears to be a 1993 model with mirrors from a 1995 or later model. The Agents also are seen in this same car. Then the next interior scene of the Agent's police car shows then driving a 1994 or later model. The brief scene of the Agents following the Cadillac when the Twin is fighting in the car, shows the Agents driving a 1994 Caprice with side mirrors of the 1995 or later model years. Then when the Agent exits the Caprice to get on the roof, it is a 1995 or later model with the Impala style rear quarter window. When the Agent is firing at and bumping the Cadillac, the Caprice is a 1993 model with the mirrors of the 1995 or later years. Then the Caprice that crashes into the cushion barrels is a 1995 or later model.
At the beginning of the movie, a security guard checks out in a scene with a set of lockers in the background. The next take shows him coming out of a building with a full office and large windows in the place of the lockers.
When Trinity is riding the motorcycle the wrong way along the highway, three police cars join from the off-ramp and travel along the side of the road immediately behind her. As Trinity swerves into traffic, an oncoming car moves right to avoid her and yet doesn't appear to hit a police car.
In the freeway chase, Agent Johnson jumps from an overpass onto the top of the truck carrying Morpheus and the Keymaker . Just before the truck goes beneath the overpass, a freeway distances sign (Whipple Ave ½, Woodside Rd 1-½, Marsh Road 3-¾) is briefly visible. As the truck emerges on the other side, the same sign appears again, behind Johnson, to the right.
During the car chase, the twins shoot out most of the windows in the car that Trinity and Morpheus are driving in. But when seen from the inside of the car, the windows are intact and there is no shattered glass to be seen.
During the freeway chase there is a shot over the shoulder of one of the twins as he shoots at our hero's car. He rakes his stream of bullets from left to right following the car as it passes behind a white van, but there are already bullet holes in the van *before* the stream of bullets ever reaches it.
When Neo meets the Oracle and she hands him a candy, she holds it out with the candy held between her fore- and middle fingers. When the camera shifts it is cradled in her palm, and then back to between her fingers.
When Agent Johnson and Morpheus are fighting on top of the truck and Johnson hits Morpheus so does a huge back flip and at that moment a car passes the truck and on the back window of the car you can see the reflection of an exit sign, Morpheus completes his back flip and he is about to loose his balance, at that moment we see no exit sign for "miles".
One twin fires at a gold Chevy Tahoe that has come between his vehicle and Trinity's Cadillac. As we cut away, no shots have hit the roof of the Tahoe. When we cut to the front view of the car turning over, it has fifteen bullet holes in five neat rows in the roof which can not have appeared during the brief close-up of the gunman between the two shots.
During the Agent Thompson/Morpheus fight on top of the semi trailer, there are multiple shots in which the Keymaker should be visible but is not. The most noticeable is when Thompson flips Morpheus in the air and he lands on his hands at the edge of the semi trailer.
During the highway chase, Morpheus lands on the hood/windshield of the Firebird driven by Niobe. As he lands, the windshield cracks noticeably. During the time she whips out around the semi and pulls right in front of it, the cracks disappear and reappear.
In the highway scene when Trinity is driving the Cadillac in the shoulder, agents try to ram her car, smashing the left rear view mirror. Moments later the agent is seen doing the exact same action and the left rear view mirror crumples again.
In the car chase scene with the twins, right when the gold Tahoe gets between Trinity and the twins, a sign can be seen saying that Paterson Pass is 1/2 mile away, in the opposite direction. This sign is visible looking from the front of the car to the back. When they force the squad car into the water barrels and get off the highway, it is at Paterson Pass and they have not turned around.
In the Chateau fight scene, when the Merovignian's henchmen line up to shoot Neo, there are clearly six of them. However, during the ensuing brawl, only five are killed on-screen (head smashed with spiky flail, stabbed while sword fighting Neo at the top of the chateau, accidentally stabbed by the guy with the trident, accidentally smashed by the guy in white's mace, and head smashed by Neo after being disarmed) and the body of the sixth henchman is no where to be seen.
After Agent Johnson slams onto the hood of a car in the highway chase sequence and the car makes a forward pitch-flip, another car behind it (screen right) makes a left roll-flip, ostensibly because of the collision with the first car. Just to screen-right of the pitch-flip car and under the right tire of the roll-flip car, the black ramp it rides on that causes its right side to lift can be seen.
After the Nebuchadnezzar enters to Zion for the first time, Neo, Trinity, Link and the Boy are walking through the deck. Neo's head connector is missing in several close shots of the back of his head. It is later seen that Neo's head connector is hidden beneath his hair, rather than visible from the back.
Before Neo enters the door that leads to the Source, the Keymaker says he can't fly to the center of the grid in 5 minutes, but after that Neo saves Trinity flying to that exact same place, which he does in a few seconds.
Morpheus has 36 hours to recharge his ship. Until then, Ballard will wait for a signal from the Oracle in his place. Since Morpheus can't leave Zion before 36 hours and Ballard can't give news from the Oracle before that time too, it makes no sense that everybody starts moving because Ballard at last brought this signal.
During the highway chase/fight scene, the traffic is moving toward the camera but there is a "Speed Limit 65" sign also facing toward the camera, revealing that ALL the traffic is moving the wrong way on the highway.
In the Burly Brawl, near the beginning, Neo throws a kick at an Agent Smith Clone and the camera follows it horizontally as it flies into another clone before colliding. The first Agent Smith flies off while the one it collides into flips towards the ground. Viewing in slow motion, the prosthetic wig on the actor flies off and stays attached to his head, comes on, and flies off before finally coming on as he hits the ground. Better visible in slow motion, but at another scene after this one, you can also see many of the wigs fly off the actors as they fly back.
In the highway chase scene, when the agent leapfrogs onto the hood of a moving vehicle (which crushes into the ground in slow motion), you can see that the only light source is the sun, which is perpendicular to the highway (low and off to the right), and all objects in the scene are casting long shadows only to the left. The agent casts his long left shadow (which extends from the edge of the car's shadow as he lands on it), but also casts a second shadow just below and behind him directly on the car's hood. He is the only object in the scene that casts a downward shadow.
On the highway chase scene, after the agent jumps onto a car and then onto another car, the first car flips over and goes in slow motion you can see the roll bars and other equipment in the car, also there is no driver.
In the Burly Brawl scene, as the many Smiths dog-pile Neo, the shots cut from a wide angle of the dog-pile, to the close up of Smith speaking to Neo. The green-tinted lighting in the close up shots reveal them to be live-action, while the wide angle shots are of a normal tint and obviously computer animated.
In the highway chase scene an agent leapfrogs onto the hood of a moving vehicle which crushes into the ground and flips over in slow motion. As the car flips it can be clearly seen that it's drive train and gas tank are missing.
When one of the twins is chasing trinity, Morpheus and the key maker, the twin's arm gets caught in the door and his arm gets shot, then when the door is let go, he heals his bloody arm, but it is bloody on his other arm.
After Morpheus gives his speech in Zion and the music starts Neo is waiting for Trinity. When he moves off to meet her in the background two people are passing and a woman is knocked against the 'rock' wall which wobbles with the impact.