When Neo meets Trinity for the first time in the nightclub she is close to him talking in his ear. Even though she pauses between sentences the shot from the back of Trinity shows that her jaw is still moving during the pauses.
Morpheus specifies the human body generates 25,000 BTUs of body heat. The human body is constantly outputting heat into the environment so he should specify the rate of energy transfer rather than a total amount of energy being transferred. Or he should specify how much time it takes for a human body to output 25,000 BTUs in order for any claims, regarding how much energy is extracted from humans, to be meaningful.
Morpheus states that a human "generates more energy than a 120V battery". The voltage of a battery says nothing about its energy content on its own; for that, the battery's ampere-hour rating is needed.
The streets all have Chicago street names (as observed in Trivia section), including Balbo Avenue. This street name is spelled correctly on signs in the subway station where Neo fights Agent Smith, but Tank directs Trinity and Neo to go to "Balboa" (as in Rocky (1976)). The DVD captions of Tank's dialogue also show it as "Balboa."
An error in language really, the Oracle at Delphi (in Greece) prophesied with the words 'Know Thyself' above the entrance to the Temple of Apollo situated there. But these words were in Greek, 'Gnothi se auton', not the Latin appearing on the sign in the movie. It is incongruous to change the language for the film as the classical reference to The Oracle is then obscured for no reason.
The name of the software company Neo works at is spelled "METACORTEX" on the outside of the building, but a sign inside the building has it spelled "META CORTECHS". Featurettes suggest that the name was changed to avoid an expensive legal issue; evidently one of the signs was missed.
The doorknob at the Oracle's apartment is installed backwards. The screws are on the outside of the door, allowing a passer-by to take off the plate and remove the doorknob. Normally the screws would be on the inside to prevent this.
When Morpheus is running towards the helicopter after Neo decimated the room with a minigun, Agent Smith walks in and fires his weapon through the wall, hoping to hit him. He shoots at a downward angle, but when we see the bullets pass by in slow motion, they are parallel with the floor.
In the first scene in which Neo appears, we see him from above, sleeping in front of his computer. The keyboard he is using is a Microsoft Natural Keyboard Pro with the atypical curved key configuration. When messages begin appearing on his screen, he tries to stop them by hitting various keys, but the close-up of the keys show keys from a standard keyboard that are clearly not the keys on a Natural Keyboard Pro.
When Neo first meets Morpheus, they shake hands. We see Morpheus from behind, and his left arm is behind his back. Then we see Morpheus from the front, and his left arm is straight down at his side. Then we see Morpheus from the back again, and his arm is once again behind his back.
After Trinity crashes through the window, tumbles down the stairs and then points her guns back toward the window, we cut to a close shot of the top of the stairs showing a hanging light fixture swinging back and forth. A few seconds before, during an over-the-shoulder shot from Trinity's perspective, the fixture is perfectly still. The sound and image imply that it did not start swinging until she reached the bottom of the stairs.
When Neo has hundreds of acupuncture needles in his body, needles disappear from his head. The comments on DVD indicate that all of the needles were a prosthetic device except for the ones in his head. The real needles are there when the camera looks at him from the side, but then disappear as the camera moves in.
Near the end of the subway fight scene, Agent Smith throws Neo into a wall after which he falls onto the rails along with debris from the wall, but when Neo backflips onto the platform, the debris is neatly positioned by the wall.
When Neo passes through the metal detector before the lobby shootout, the side profile shot as he is stopped by the guard has him with his jacket halfway open. He is clearly unarmed as he is wearing a normal belt and there are no guns under his jacket. However, he then opens his jacket from a completely closed state to reveal that he is wearing a fully loaded gun belt with both weapons and ammo.
When Agent Smith is interrogating Morpheus, he has his hands on his head, his index finger is in front of his ear in the shot from behind, but in the shot from the other direction, his index finger is behind his ear.
Just before the door to the Oracle's apartment opens, Morpheus has his glasses on. After the door opens and the camera angle switches, his glasses are in his left hand (visible after Neo crosses in front). Presumably he snatched them off in the same move that instantly took his arms from a 90-degree angle to straight down.
When Morpheus and Neo move from the dojo to the jump program, the shot from their viewpoint looking down shows them landing far from any roof structures, on a building much higher than any nearby. The next shot of Neo shows them to be right next to a structure, on a building about as tall as one right across the street.
As the team prepares to visit the Oracle, we see Tank "loading them up" pressing buttons on the various keyboards around him. Before the last cut, his right hand is up, pressing buttons while his left hand is down. When we cut to the shot above Tank, his left arm is up and his right arm is down.
After Neo steals a man's cellular phone and the agents shoot at him, we see him running down an alley with the back of his shirt untucked from his pants. As he kicks in the door, his shirt has tucked itself back into his pants.
When Neo is in the old Lincoln with Trinity, Switch, and Apoc, Trinity says, "Apoc, lights." A close-up of the light switch follows. The external lights should be off because the switch is all the way in, yet it is night and the lights have been shown to be on. Apoc then pulls the switch halfway out, which would turn on the exterior running lights only, not the interior lights. He should've turned the switch, not pulled it.
When Neo is interrogated by the agents, the reflection in Agent Smith's glasses do not correspond to the action in the editing. For instance, we see Neo standing in one shot, but the reflection in Agent Smith's glasses shows Neo sitting in the next shot.
When Neo is flushed from his cubicle and fished up with the claw from a hatch in the Nebuchadnezzar he is passed out. But as he enters the ship he clearly moves his feet to avoid hitting the rim of the hatch.
When Morpheus escapes the military building he snaps his handcuffs but they remain on. When Neo grabs Morpheus, in mid air, no handcuffs are visible. The handcuffs re-appear when Neo drops Morpheus onto one hand.
When Neo opens fire from the helicopter, and the glass begins to break, none of the three agents is visible (though they should be) and the chair in which Morpheus should be sitting can be seen to be empty.
As Morpheus introduces Neo to the Construct, his glasses are completely dark. The following shot they suddenly turn highly reflective. This was because, for that shot, the glasses were painted black to avoid the cameraman from being reflected in them.
After Neo is brought into the real world, Tank comes to introduce himself; while they're talking, the strap on Tank's right shoulder repeatedly jumps from the middle of his shirt sleeve to the edge between shots.
In the building the group returns to after seeing the Oracle, smoke appears around the hardline before it's cut by the agents (or by one of their minions). Also, the amount of smoke is considerably more than wires that size could produce unless they were already on fire.
In the scenes after Neo lands on the roof from the helicopter, you see the helicopter in the background with the main rotors spinning. In the next shot, Neo's back is to the camera with the shadow of the helicopter on the roof of the building, but there are no helicopter rotors fixed, or spinning.
When Neo enters the Matrix for the first time on the Nebuchadnezzar with Morpheus, as he sits in the chair we clearly see Trinity lock his feet in place. But when Neo pulls himself out of the Matrix during that same visit, he jumps out of the chair and no one can be seen releasing his feet.
Right after the "Dodge This!" line, Trinity shoots the agent in the head. When she says this they show the agent look to the left and you can see the gun at the side of his head. When the camera pulls away after she fires and shows the agent falling, he is falling backward and lands on his back. You can see the bullet hole in the SWAT officer's forehead when the agent loses the connection. Even if he turned his head, he still wouldn't have fallen backwards perfectly like he did.
During the scene where Cypher is sitting on Morpheus after betraying him, Morpheus is still plugged into the Matrix yet clearly blinks just before the scene cuts away. It is visible even though the camera is not showing his face.
When Neo does the famous "Matrix" move, where he bends back, but still on his feet while the agent shoots at him, he drops his guns right beforehand. But while he's commencing the move, as the camera circles around the actor, you see no pistols anywhere near him. But just as he falls the pistols are right beside him.
When Neo and Trinity board the helicopter to go after Morpheus, Trinity is not wearing any gloves. A minute later, when Trinity is piloting away from the building with Neo and Morpheus dangling from the helicopter, Trinity's hands are shown on the controls and she's wearing gloves.
When the bomb is detonated at the bottom of the elevator shaft the lobby is shown to be in pristine condition immediately before the explosion. However, the lobby should be in shambles due to the previous shoot-out. This is most noticeable when looking at the pillars after the shoot-out and during the explosion.
When Trinity crashes through the window and tumbles down the stairs, she's oriented facing forward and should land face down. But when she rolls to a stop and points her guns back toward the window, she's face up.
When Neo, Trinity, Cypher, Switch, and Apoc are escaping the building, and under fire from the SWAT team: Apoc and Switch burst out of the wall in the basement, and neither are wearing their sunglasses (they abandoned them before entering the crawlspace in the wall). Yet, when Trinity opens a grate in the floor and they escape through it, Apoc is clearly wearing his sunglasses again.
In the initial release of the movie on VHS tape, when Neo gets the mobile phone from the FedEx courier to talk to Morphius for the first time, a crew member's hand and forearm are clearly visible in the background. This was corrected in subsequent releases on both VHS and DVD.
When Morpheus is showing Neo the "Real World" as he is sitting in the chair he looks up into the sky, in the reflection in his glasses you can see some crew members, a boom mic and some lighting before the camera looks upwards.
When Neo is firing his two custom Skorpion SA Vz 61 submachine guns during the lobby shoot out, the shot showing the casing falling to the floor shows rifle casings, likely 7.62x51mm NATO (.308 Winchester), when the Skorpion fires much smaller .32 ACP pistol rounds.
During the flashback scene where Morpheus is describing to Neo the "peak of civilization", cars can be seen driving on the left hand side of the road. This is due to the filming location being Sydney, Australia; and in fact that footage is of the Sydney Harbor Bridge.
The chain of ammunition for the gun in the helicopter does not feed directly into the gun; it goes through a feeding mechanism between the ammo box and the gun. Further, the shells that drop are indeed spent; they have a bottleneck shape that confuses some viewers.
During the rescue of Morpheus, at one point Trinity is seen to use both hands in controlling the flight stick of the helicopter. While a helicopter normally requires use of two sticks to control, in the kind of emergency situation shown, the collective (controlling up/down motion) can be temporarily ignored.
On Neo's introduction to the Construct, Morpheus jacks him in, then shows up in the Construct himself almost immediately, far quicker than he could have jacked in himself. But it's quite possible Neo was held in some kind of limbo until Morpheus was ready to join him.
The physical effect of Neo's lifetime in a pod are understated, as his body would be much more severely atrophied from use. However with this error in place, he would not be as helpless as a "newborn baby". The physiology required to walk, comprehend vision and sound, control bowel movements, speak etc. is well-developed by birth, with the later development taking place in the brain as the child matures. Therefore it's a reasonable (if speculative) suggestion by the movie that these mental abilities would be retained by someone who first learned to do them in a "simulation" hooked into his brain, even if he had not made use of them. Note particularly that even intravenously-fed individuals have to defecate and urinate, which given that Neo doesn't have any "plugs" for a colostomy or catheter means these functions of his body would have had plenty of practice.
No guns in this movie can be fired as fast as they are. The bullets can be seen flying in bullet time and the action flies back, but the action wouldn't fly back until the bullet was through the target and wouldn't go that fast. While this is true in reality, the scenes in question take place in a computer defined world where the guns can fire as fast as the computer will allow.
When Neo is being interrogated by the agents, Agent Smith plops a folder on the table. When he opens it, there are no pages on the back of the cover. When the camera shifts as Agent Smith is looking through the pages, we see several pages on the back of the cover that Agent Smith never placed there. However, the folder is an obvious reference to computer folders and the scene is a showcase for the fact that Agents are not human, but can manipulate things as computer programs. The visible world is merely an interpretation of their digital actions.
When Neo is rescuing Trinity from the falling helicopter, he slides across the roof of a building. When he reaches the edge, his foot hits the block causing it to move, but in a way consistent with a real block whose grout is imperfect; after all, that's a rather large force.
The Massive Attack song "Dissolved Girl" playing in Neo's headphones is track 6 on the album, not track 5, and the timing on the counter is off in relation to the actual song. Given Neo's equipment, it could well have been a homemade custom CD.
The second time Morpheus calls Neo, he tells Neo the line is tapped, and asks him to go to meet Trinity at the Adams St. bridge. If the line was tapped, the agents should have had plenty of time to get to the bridge themselves.
The reason why the machines use humans (a power source) makes no sense from a scientific point of view. The useful energy extracted from the humans would necessarily be equal to or less than the energy expended in keeping them alive, even before we consider the energy expended in running the Matrix. An alternative is provided in the novelization and the spin-off short story "Goliath": the machines use human brains as computer components, to run "sentient programs" (the Agents and various characters in the sequels) and to solve scientific problems. Fans continue to debate the discrepancy, but there is no official explanation.
During the fight scene between Neo and Agent Smith in the subway station, after Neo incapacitates the agent and flips out of the way of the oncoming train, you can see where the wire harness connects to his back. You can also see one of the wires visible by his wrist.
During the bit when Trinity's helicopter is crashing, right after Neo says "Trinity!" there is a shot of the helicopter in slow motion falling and disappearing under the ledge of the building Neo is standing on in the foreground, with the building that it's going to crash into behind. However, the helicopter is not reflected in the building's windows.
When Neo is fighting the agent in the subway scene, they shoot at each other in bullet time. Though there are bullets coming out of the pistols, the actions of the pistols (the top part of the gun that slides back to allow the spent cartridge to spring out of the barrel) are not moving to let the pistol reload. In spite of this, the slides are locked back once the guns are empty. In addition, there is no recoil.
When Morpheus fights Agent Smith in the dilapidated bathroom, Agent Smith knocks him over onto an old toilet. Before Morpheus's head hits the toilet, the outline of the section which is about to be "knocked out" is visible. Also, the toilet can be seen to bend and wobble as Morpheus falls onto it, revealing it to be made of rubber (or at least something other than porcelain).
In one shot where Neo fires the chain gun at the Agents, one jumps out of harm's way while firing his pistol. While there is a flash, the pistol's action does not go back and there is no recoil like there should be, revealing it to be added in post-production.
When Neo is being run through the agent training program with the woman in the red dress, Morpheus' sunglasses reflect Neo with a Desert Eagle pistol being held up by an Agent standing in an empty sound stage, not the busy city they're supposed to be in.
When all the people are in the wet-wall and Trinity pulls Neo and they all fall. They drop to the bottom and there is dust and debris everywhere. But through the dust you can see Trinity (or her stunt-double) come down and be pulled back up, like she was on a bungee cord or something. Her back arches and you can see the "bounce" as she is pulled back up.
As Neo and Morpheus dangle on a cable beneath the helicopter, one can clearly see the black cable running from Neo's waist, down Morpheus' arm, and under his sleeve to connect to a concealed safety harness under his clothing.
When Neo is fighting the agent in the subway, and he is leaping out of the subway's path, you can clearly see him grasp the wires that are hoisting him up. He pulls on them to make the backflip onto the platform.
When Neo gets the message on his computer to "follow the white rabbit", there is a knock on the door. When Neo opens the door, its clearly visible that Neo is wearing lenses of different colors. One eye is jet black and the other one looks green.
The goof items below may give away important plot points.
During the chase scene at the end of the movie, Neo steals a phone from a man in a black suit. As he runs off, the man starts shouting and pointing at him. When we see the man from behind, although he's still shouting in the same voice, the actor is clearly Hugo Weaving as Agent Smith, with his gray suit and different hair cut. The sound effect to indicate the transformation into Agent Smith isn't played until quite a few seconds after the change of actor and costume.
Cypher discusses handing over Morpheus with Agent Smith at a restaurant in the Matrix. However, it's taken for granted someone would have had to jack him into the Matrix and back out of the Matrix. He or she would have also known that Cypher was conversing with an Agent by reading the Matrix code. Cypher's betrayal would have become known. Although the movie doesn't make it clear, Cypher was able to set up the system to jack himself in and leave again automatically. This is what he's doing when he's interrupted by Neo, which is why he shuts off the monitors immediately.