Continuity mistake: When Neo is fighting the three agents at the beginning of the film, the ground is really dirty but when he flies off, there's only some papers and the ground is dirty again after that.
Continuity mistake: In the scene where Trinity is driving on the freeway, you can see from the interior shot that her door is locked. In the exterior shot you can see her door is unlocked. This is consistent all the way through the driving sequence.
Continuity mistake: In the middle of the freeway chase scene when Morpheus is on the overpass, in one shot the twins SUV has already made it round the bend of the overpass. The following shot they are going around the bend again. (01:25:40)
Continuity mistake: In the scene just before the big 100 Agent Smith's fight, we see Neo and the Oracle talking on a bench. In one shot we see that the Oracle has her arm on the bench's back, then in the following shot we see her put her arm down by her side or on her lap, then in the following shot after this its back on the back of the bench. (00:45:10)
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.
Revealing mistake: In the scene where Neo is fighting the 100 Smiths, there's a shot of Neo baseball-smacking a Smith into a set of windows. While the scene is a bit blurry, it's pretty apparent that the Smith literally falls apart when he hits the window, like he was made of sausage links. (00:57:15)
Other mistake: In a scene during a power cut, car headlights also go out.
Revealing mistake: When Neo fights the Agents near the beginning, he knocks out the first by knocking him into the wall. He then knocks the second into the wall by spinning round on the third Agent's back. After the shot of the second Agent hitting the wall both Neo and the Agent go from standing completely still displaying a clear "Action" cue. (00:10:00)
Visible crew/equipment: After Trinity and the Keymaker have jumped onto the lorry, Morpheus walks forward with his sword. In the shot of his upper body you can see the crew in his glasses. (01:25:35)
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: Near the end of the film when we see the Keymaker open the door and Neo kicks Smith to make a gap, if you look where Neo is, there are two Agent Smith's behind him, they are looking towards Neo's direction and pulling there guns out, yet when the shot changes to a close up, the two Agents are facing one another and then pull there guns again. (01:44:10)
Continuity mistake: In the freeway chase, just after the brown 4x4 flips over, one of the twins is shooting at Trinity's car. In a shot from the front his head's well above the sights, and he's spraying bullets around a bit. From behind him, he's holding it tight into his shoulder and keeping his fire in one place. (01:22:15)
Revealing mistake: On the freeway chase, when the agent jumps on the bonnet of the car and it flips over, check the underneath. There is no exhaust pipe and a reinforcing frame runs either side of where it should be. (01:23:45)
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: On the freeway, the rear lights on Trinity's bike are sometimes on and sometimes off. And, no, they're not brake lights because they're on at the start when she is accelerating away from the lorry that is transporting the bikes. (01:30:35 - 01:31:40)
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: When Trinity and the Keymaker jump off the truck on the motorbike there is a white car seen just in front of them. In the next shot from behind them driving, the white car has gone. (01:26:50)
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.
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.