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.
Suggested correction: There were 3 police cars; two Impalas and a Caprice. The police car possessed by the agents was always a Caprice from the beginning. One of the Impalas rammed into the black Oldsmobile Intrigue which was shot and flipped by the twins and the other Impala disappears after the massive crash scene (probably crashed within the mayhem).
The Impalas were ahead and the Caprice was behind in the tunnel before the highway. Right after the highway scene (when the CTS Swerves between two trucks) however, you can see 5 cars (one Caprice and three Impalas, and one unknown car ) but after that it's back to 2 Impalas and Caprice. So the mistake is three cars turning into five, not the switch between Caprice and Impala.
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.
Suggested correction: Who says the door was bullet proof and the Keymaker couldn't have been shot through the door?
The point of the stupidity is that he shouldn't have been in the doorway at all, even if the door wasn't bulletproof, there was no need for him to even stand behind the closed door. He could have pushed the door closed from the side.
It seems to be a heavy door, he simply couldn't close it with just his arm, thus he had to move his body forwards in order to close it. In that brief moment he got shot before the door closed. He could have for example kicked the door shut but he simply didn't think of that at that moment, also not knowing the Smiths were about to fire a volley of bullets at them.
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.
Suggested correction: Who says he's dead? It just got knocked down.