Continuity mistake: Sati and her family leave one suitcase when they get on the train (the one Neo was carrying), but when the train comes back and Trinity steps out, there is no suitcase. It can't have gone anywhere - as we see when Neo tries, the only way out is on the train, otherwise you're caught in a loop.
Continuity mistake: At the very end when Oracle is sitting on a park bench, she and Sati look at the sunrise between some skyscrapers. About a minute later, there is another shot of the sunrise, but in this shot the skyscrapers are considerably shorter.
Continuity mistake: Towards the beginning of the Super Burly Brawl scene (right after Agent Smith gets knocked down on the road), Agent Smith and Neo fly up in the air and collide with each other, causing a massive surge of water to spread out as if a bomb went off. The water then falls back down on the Agent Smith clones, who are now looking up. But if you pay close attention it seems like they are completely dry, despite the fact that they have been standing in the rain and are all soaked.
Revealing mistake: In the scene where Captain Mifune is defending a bridge, alone, and commands "reload", he put the right arm of the APU straight, revealing in the background some sparks that floats independent of the action and stops for a few moments.
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: When Smith is finally destroyed there is a wide shot and a close shot of the Oracle lying in the water filled crater. In the wide shot, there is a lot more water; her arm is completely underwater and so is half her face. In the close up, her head is almost entirely above water and her arm is visible.
Continuity mistake: At the start, When they're running a search for Neo in the Matrix, Morpheus' arms keep switching. For example, in one of the closeups, his arms are by his side, when in the previous shot it's rested on his chin. And when that guy comes in and says 'Sir, I've got the projections,' his arms are folded.