Continuity mistake: In the scene where Neo meets the Oracle before the Burly Brawl, just after Neo looks at Seraph and says "so's he", from behind she is leaning her head on her hand, with her hand by her jaw. Then when we see her from the front (instant cut, no time she's not visible), her hand is against her temple when she says "keep going".
Revealing mistake: In the freeway chase scene when one of the agents jumps onto the hood of the first car then jumps off, the car flips, then a second later as the car is still flipping you can see the gas tank and transmission have been removed.
Visible crew/equipment: During the scene where Neo is talking to Agent Smith in the park area where Neo was talking to the Oracle, there is a close-up on Agent Smith's face. In his sunglasses you can see a bright white screen to reflect the light onto the faces of the actors. This isn't visible in any non-reflected angles. You can also see the cameraman on the other side.
Continuity mistake: During the freeway scenes, the katana Morpheus used as a foot hold to grab the keymaker keeps moving. It was at arm's length from the top when he inserted it; when Morpheus was standing on it, the sword was a whole body length below the top; when Morpheus took the sword out in his fight against the agent, it was back in its original position.
Continuity mistake: In the highway chase scene there is a shot of the police cars before they get onto the highway and the cars are Chevrolet Caprices. When they are on the highway chasing Trinity's car, the police cars become brand new Chevrolet Impalas. But when the police cars start to ram her, they become Caprices again.
Continuity mistake: During the car chase, the twins shoot out most of the windows in the car that Trinity and Morpheus are driving in. But every time they cut to a shot of them inside of the car, the windows are intact and there is no shattered glass to be seen.
Continuity mistake: In the car chase scene, when Trinity is driving the cadillac, the Agent in the cop car slams into the driver's side of Trinity's car and the driver's side mirror is bent inwards. When Trinity drives the cadillac onto the exit ramp, the driver's side mirror is back in its normal position.
Visible crew/equipment: In the scene where Morpheus is sitting in the chair near the end of the movie giving his "War and fate" speech you can see the microphone and camera in his sunglasses. This is repeatedly seen during the whole scene.
Continuity mistake: During the freeway chase scene the Cadillac gets slammed up against the wall and sparks start shooting from the side to show that the car is being scraped by the wall. However, in several quick shots after we see the car gets scraped against the wall, there are only bullet holes and no trace of scraping against the side of the car.
Continuity mistake: Trinity's cut on her right arm disappears and reappears throughout the freeway scene.
Revealing mistake: When Agent Smith stands in the way of Neo, Morpheus and the keymaker, Smith's glasses reflect an empty corridor when 3 people are right in front of him.
Factual error: In the scene where Neo is shot at by the French guy's henchmen, they shoot with different types of guns. 4 of these are submachine guns which would fire 9mm. Another is a M1928 Thompson would fire .45 APC. Lastly there is a Heckler and Koch G36K which would fire the drastically different 5.56x45mm NATO. When Neo stops the bullets, they are all 9mm Parabellum rounds.
Continuity mistake: Further to the comment about some of the Smith clones not having Hugo Weaving's face pasted onto them, just after Neo does his back flip into two agents whilst kicking the two either side of him, just after he turns back around towards the camera, there is a very obvious stuntman standing just behind him who looks absolutely nothing like Agent Smith.
Continuity mistake: When Neo and the keeper are fighting on the middle bench, one by one the bowls get knocked off - the two on the far corners (left and right) reappear and disappear at least once. Likewise the pot on the right hand table with stick-like things in - that table's completely cleared at one point, but that pot reappears.
Revealing mistake: 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.
Deliberate mistake: When Morpheus is facing the twins' car, the road's not all that wide, and there are concrete barriers both sides of him. After he rolls to the side and slices their car, we see a side shot, quite far back from the road, and the barrier closest to the camera has disappeared (presumably so we get a better view). In a closer view, both barriers are back again.
Continuity mistake: In the scene where Neo fights the Merovingian's henchmen he plunges a sword into one of them and pushes him off the balcony and jumps with him. The body falls near an already dead henchman. In the next shot when the others jump off the balcony the body with the sword is away from the first body.
Continuity mistake: When the twin leaves the car that Trinity is driving, he is standing on the freeway by himself. You see a flat-bed truck, then a police car, then a red van pass him by. But when they show the shot ahead of him, the truck is still there, but the cop car and the red van are nowhere to be seen.
Continuity mistake: In the car chase scene when the Twin enters the car with Morpheus, Trinity and the keymaker the camera view changes between aerial shots and shots from in the car. In the aerial shots the road behind them is completely empty. From the shots in the car you can see several cars behind them through the windows.