Other mistake: In the freeway scene, when an agent takes over the black truck, he turns around to go the other way. As he does this, there is a shot from the side of the truck as he turns. In this shot you can see that the front of the truck will easily crash into the wall, but cuts away before it does.
Other mistake: In a scene during a power cut, car headlights also go out.
Continuity mistake: In the car chase scene, when the black car flips, a bullet spark can be seen on Trinity's car. The only thing wrong about this is that the bullet sparks on the windscreen and leaves it undamaged.
Continuity mistake: When The Architect is talking to Neo, the tie tack he's wearing appears to have fallen out of the left collar (right side on the screen) in one shot. Seconds later, it's back in place.
Continuity mistake: In the rotating shot around the semi-truck, in the freeway scene, the sword that Morpheus stuck in the side earlier (and uses later that scene, so it can't have fallen out) is nowhere to be seen.
Continuity mistake: In the Burly Brawl, when Neo is getting the pole out of the ground, there is a sign behind him on the wall next to the barred windows, but when Neo jumps and spins with the pole, in the background you see that the sign has vanished.
Continuity mistake: When Neo is fighting the Agent Smiths, he kicks one into a multi-paned window. It is visible in several shots but the hole disappears several times.
Continuity mistake: On the long straight shot of the two trucks driving at each other there is a clear starting/ending position for the busy traffic, followed by empty road.
Continuity mistake: When Trinity is driving down the freeway, the bullet holes in the right side of the car are not there on several occasions when the car comes into view from behind other vehicles.
Continuity mistake: In the highway scene when Trinity steals the bike from the truck, you can see that the bike's tires are completely clean while the bike is in the air and in the next shot just before the bike touches ground the tires are now all dirty.
Continuity mistake: In the freeway chase scene just before the two trucks collide, Morpheus and the Keymaker are at the front of the white truck (you can tell because otherwise you wouldn't be able to see that much of them in the final front shot), but when they're catapulted forward they're right at the back.
Revealing mistake: 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.
Continuity mistake: In the freeway chase scene, when the agent jumps on the intermediate car, it flips over. During the second slow-mo shot of it tumbling end over end, a bent piece of the bumper can be seen to leap UP from the ground, become un-bent, and attach itself back onto the car. This process is also visible for several other small pieces of debris on the road. It is NOT simply broken glass bouncing upwards - the bent bumper reassembles as it leaps up, and small metal shards suddenly go from motionless to flying towards the car. Broken glass moves as it would be expected to: away. It seems that the glass may have been edited in later.
Continuity mistake: Right before the highway chase scene, when the Key maker says, "Always another way", if you look at his head, he has a full head of hair. When Trinity and the Keymaker jump off the bridge onto the motorcycle truck, you can see the Keymaker has a bald spot and a little less hair.
Visible crew/equipment: After the BIG crash during the freeway scene, if you look closely from Trinity's Ducati you can see the paramedics, cameramen, and equipment.
Deliberate mistake: In the scene where Trinity jumps out the building with machine guns and an agent right behind her, we see that while they are exchanging bullets, her hair is slick back and wet. But once she is shot and falling down freely, her hair is dry and flying freely.
Continuity mistake: During the Burly Brawl (Neo VS 100 Agent Smith clones), there is a point where dozens more 'clones' burst through the doors of two buildings. In one shot you can see that the number of clones simply ends, and no more are coming after a point (very briefly at the end of one of the first shots), but in the overhead shot shot, there are suddenly more and more Smiths pouring out at a constant rate. There is not even a pause in the Smiths coming out, so it makes no sense.
Continuity mistake: When Morpheus faces the Twins' car with his katana, there is a shot from the side (the same shot where the side of the bridge disappears) where a part of the highway below is visible. It's completely empty while only seconds before you can see the highway full of cars.
Revealing mistake: Just as Neo begins fighting in the "Burly Brawl," take a look at the Smith to the right of him (he puts his hand on Neo's shoulder I think). The face is not Hugo Weaving's but the face of the stunt person. Looks like the effects crew forgot to put Weaving's face on that guy.
Continuity mistake: Before the freeway chase and a little bit after they leave the garage, the twins shoot and crash the BMW, then Trinity's car turns right and drives off. In the next shot, the CTS is parked in the corner.
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.