Continuity mistake: In the scene where Neo sees the oracle at her home, as the shots go back and forth during the dialog immediately after she sits down, her cigarette pack goes from closed to slightly open several times, until she takes a cigarette, then it stays slightly open.
Revealing mistake: In the subway scene, when Neo gets slammed towards the wall (and crashes into it) it's visibly Keanu's stunt double.
Revealing mistake: During the battle of the dock, just before Shara takes her second shot at the digger, she is seen from behind as her weapon is being loaded. As Zee is about to slide the rocket in, the green screen is momentarily visible through the barrel.
Continuity mistake: In the scene where Bane has the scalpel to Trinity's neck, the bloody mark below it keeps disappearing and reappearing. The scalpel changes positions too as well as the blade itself changes.
Continuity mistake: When Trinity is meeting with the Frenchman, the olive in his martini changes. In the first close-up shot, he only has one green olive on the cocktail stick. From then on he has two, until he eats one.