Link: Trinity, we're talking less than five minutes here.
Trinity: In five minutes, I'll tear that whole goddamn building down.
When Neo is meeting the Oracle, as well as when he's fighting the Agent Smiths right after, there are a bunch of words spray-painted on the fence, walls and bench, two of which are "one", spelled upside-down and backwards, and "role", which has to do with everyone having a role, or purpose, to play in and/or outside of the Matrix. See more...
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Continuity: At the start of the Burly Brawl when we see Smith throw Neo through a bench, when Smith goes up to jump on him, from this point of view, the two or three steps behind the bench are nowhere to be seen, yet when Smith lands on the ground, the steps are probably less than a foot away from the bench.
Revealing: After the twins shoot the black Oldsmobile, it hits a barrier and does a spiral, and lands on its roof. That's impossible because the car's fender would have been torn off. It would have skidded a sharp right and went under the semi that Trinity was driving by. That indicates that there was a ramp to lift the car off the ground and do the spiral.
Continuity: At the very beginning of the film when the 3 agents burst through the door where the captains are holding the meeting, if you notice the 3 agents enter the room and stop just after the broken door, and when the agent closest to Neo says, "only human," the other two agents are now a lot further in the room, there is no time to move forward as it is between shots this happens.
Continuity: In the scene where Neo meets the Oracle, when Neo and Seraph are in the corridor with all the back doors, the small piece of wall around the door is white. However, when Seraph opens the door so that he and the Oracle can go through it, the borders of the door opposite to the open one are green.
Audio problem: After the Keymaker has been shot, Morpheus and Neo rush to him and turn him over. The Keymaker's gasping for air is very audible, but the first reflection of him that we see in Morpheus's sunglasses shows that his mouth is tightly closed. This is only visible in that one reflection shot.
Continuity: In the scene right before the freeway scene, in the city streets, the Escalade EXT rams a brown BMW 7-series in the purwuit of the Silver CTS. The BMW rips in half, but there's not a scratch on the EXT. Later in the freeway scene, you see a headlight blown out, and a katana sword can rip it, whereas a car smash causes no damage.
Deliberate "mistake": In the scene where Neo is sitting with the oracle and talking, there is one quick shot of the fence area where Smith comes in. In spraypaint on the metal fence it has "ONE" written across it diagonally up to the right. When the oracle leaves and Agent Smith comes through the fence entrance the spraypainted "ONE" has disappeared.
Continuity: In the freeway chase scene when the Cadillac is being side-smashed by the police cruiser, the agent driving the cruiser disappears from the car when the vehicle hits the water barriers. It can't just be that he changed to a different body - that would have left the original occupant still in the car.