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 beginning of the movie when Trinity and Morpheus first go to visit the Oracle, if you look behind them there are two wooden frames that are on the back wall where Seraph is, then a few shots later they are on the wall where Trinity and Morpheus walked in.
Continuity mistake: In the scene where Neo is talking with the Oracle in her apartment, the Oracle sits down at the table, picks up a bracelet, and right before the shot changes, you can see that it is on her hand, almost to the thumb area. When we cut back to her a second later, the bracelet is back on the table, and she picks it up and puts it on again.
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.
Continuity mistake: As the three start to fight at the Merovingian's club: after Trinity snaps there is a shot of Seraph pushing someone down as the man in black pulls the gun on him. To the right, there is a guy who is hurled to the floor by Trinity. In the next shot, Trinity hurls the man again.