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.
Stupidity: When the Keymaker is closing the door to the room that leads to the Source, he stands in the doorway resulting in the multiple Agent Smiths gunning him down. He could have easily closed the door without standing in the doorway and consequently would have lived.
Revealing mistake: When the Key-Maker shuts the door in the corridor-scene while being shot at by Smiths, one dead Smith-body lies in the corridor, the one that Neo knocked through the crown of other Smiths. When you look closely at the body of the Smith, you can see his right foot slowly moving.