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.
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.
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.
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.
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.
When Trinity stops the motorcycle to avoid the truck, she doesn't shift down so it's impossible afterwards to gain speed as shown.
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.
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 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.
On the freeway scene, there are many cars and trucks that were computer generated to fill in the road, but the shadows are just under the vehicles, not angled away like on the real ones.
In the 100 Agent Smith fight, you can see (especially in the larger shots) that there are many Smiths that don't look like Smith at all. Also, for the ones that have Smiths face digitally painted on them, when they turn around you can see that the backs of their heads are all different.
During the fight against the Frenchman's men, at one point a giant stone statue is broken, falls over and smashes apart. You see it hits a stone railing on the stairway, which wobbles and makes it very clear that the statue is a breakaway, unlike the rest of the set.
During the highway chase when the agent smashes the car by jumping on the hood, the shot switches to inside the vehicle being driven by the twins. The vehicle is being driven on the right shoulder of the highway where it is completely free of traffic and no crashing vehicles are in the lane or even moving toward the lane. Yet the driver swerves into the lanes where the other vehicles are crashing.
At the end of the 100-Smith fight, the Smiths are standing in a circle around Neo as he flies away but in the close of Smith Prime, none of them are in the reflection in his glasses. In fact, none of the glasses have any Smith reflections in them.
The Keymaker tells Neo, Morpheus and Trinity they must take out 27 blocks. When Trinity is hacking into the CityPower Grid with Link, she deactivates nodes 21-48 and the system asks for confirmation of deactivating 27 nodes. Except 21-48 is 28 nodes.
When Neo catches Trinity falling from the building, Link says "Oh man, He caught her" twice.
During the meeting in the sewers, a car pulls up to the building; as it slows down, the legs of a camera operator are reflected in the bumper.
During Morpheus' "very meaning of our lives" speech, the boom operator and boom mic are visible, reflected in his sunglasses (particularly noticeable in Imax format).
During the meeting at the beginning, the camera is clearly visible reflected in Morpheus's sunglasses.
A studio lighting fixture (with shield) is visible reflected in the left lens of Smith's sunglasses prior to the Burly Brawl, during every shot of Smith's face, while he talks with Neo.
When Neo is opening a door, a close-up of him reaching for the doorknob shows a camera behind him.
The first show of Smith, he drives an Audi. However, from the lamps, we can see that it's not US-Spec.
Neo gets surprised of knowing there were other Chosen Ones before him and that the Matrix is much older than what he believed, but he had already heard about this from the Merovingian and Persephone.
Agents can overtake anyone's body except those enter The Matrix from outside. On the highway chase scene, agents prefer to overtake the body of cops which are way behind during chase. Instead they could have overtake any car's driver which is just next to or in front of the car the trio escapes.
During Neo's meeting with the Oracle, she says very early on "I know you're not sleeping. We'll get to that," and then doesn't return to the subject before the conversation is over. Which kind of puts the Oracle's predictions in some doubt if she can't even predict what she's going to speak about in a short conversation.
In the previous movie, the machines' goal was to get Zion's entrance codes to destroy the city. In this movie, it's revealed the digging and the upcoming siege of Zion was always meant to happen, so it was pointless earlier to seek for the codes.
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.
When Neo talks to counselor Hamann before going to the engineering level, his plug is not visible on his neck.