When Neo is lying in the crater during the final fight, one of his ears is filled with muddy water. In the next shot we see his other ear filled with water while the one which was previously filled is now empty.
When Neo is talking with the Oracle, he says "How did I stop four sentinels just by thinking it?", when in fact, at the end of The Matrix Reloaded, we saw that there were actually five sentinels that Neo stopped, not four.
Even though Commander Locke stressed the importance of destroying the digging machines earlier in the film, no effort is made to do so when the dock is (temporarily) free of sentinels, and he seems only interested in disciplining the crew of the ship that disabled their equipment.
Even though Neo planned to peacefully surrender to the machines when he reached the city, he made no effort to communicate this to the machines via radio. Considering that Neo still had the 'codes' that the Architect wanted, and that the EMP from a single ship would barely make a dent in the city's defenses, the machines would have surely been open to a peaceful surrender, but Neo does not even attempt this, resulting in Trinity's death.
During the scene at the gates to the Temple, just after Neo has defeated Smith, when Kid realizes that Neo has saved them all, he takes off his kit, and as he turns around Captain Mifune, who died earlier in the battle for the dock, can be seen.
As the Hammer is reaching the gate to Zion, the hovercraft's gravity pads (glowing pods) switch between being damaged and fully functional. In addition, all of the aft pads were damaged at one point and the hovercraft was seen dragging the tail end on the tunnel. However, once the ship reached the gate, all pads, including the damaged rear pads, were shown to be fully functional.
When Trinity, Morpheus, and Seraph go to visit the Merovingian, the Merovingian is seen eating olives from his drink (a Martini). At first glance, there are only two olives. He takes half of a bite out of the first olive, then finishes it, then eats the second. However, just moments after eating the last olive, a third olive magically appears on the toothpick.
When Smith and Neo are running at each other in the rain for the final battle, the camera focuses behind their feet in slow motion. You can visibly see both lines of Smiths on either side of the street. However, you cannot see their opponents, just the feet of whoever it is focusing on.
Train Man fires 9 times with a six-shooter while Morpheus and Trinity chase him through the subway. Although the Train Man makes the rules in the "limbo" train station where he is more powerful than Neo, there's no reason to suppose he has the same power in the rest of the matrix where he is chased by Morpheus and Trinity. He'd have no reason to flee if that was the case.
When Seraph is trying to get out of the building with Sati, he takes her into a corridor, where the lights go out and they are left in pitch blackness. After trying a few doors in the dark hallway, he forces one open. We cut to a view inside the room they just burst into, and there is light in the corridor behind them.
Neo takes a suitcase belonging to the Indian family when the Train Man takes them away. This suitcase is by Neo's side on the platform after they leave, but when Neo jumps to the track in attempt to run through the tunnel it is farther away from him.
At the beginning of the final battle, we see a shot of Neo and one of Smith beginning to run at each other. Each of them is running so that the direction of the slanting rainstorm hits them in the face. As they are running at each other, this should only be true for one of them.
During the dock battle, when Charra is carrying the rocket launcher and Zee is loading the rockets, the front camera angle shows two empty tubes. An immediate switch to a top down angle shows Zee suddenly finish loading the second rocket.
When the machines stop attacking the survivors emerge from the dock Kid has a fine blood splatter on his forehead but his face is remarkably clean. As he runs inside he meets a councilor then goes on to announce to everyone the war is over. Both times the pattern of blood changes and his face gets more mucky.
When Neo and Trinity discuss going to the Machine World the camera shot moves from back to back to show the characters speaking to each other. When the camera is on Trinity's back 3 plugs are visible on her back. When the camera is on Neo's back there are no plugs at all.
It had been established that Neo was trapped at the train platform not being "jacked in", but lying unconscious, requiring Seraph and Trinity to bargain for his release. Later, as they are travelling through the Matrix (in the city), Neo announces he must visit the Oracle one last time. After their encounter, Neo is seen being unplugged, not lying in the infirmary.
When Agent Smith approaches Oracle, she is smoking a cigarette. She puts the cigarette in her mouth and takes a sip, but when she breathes out, no smoke comes out. She does that two or three times and not even once she breathes out smoke.
When the upside down fight at Club Hell is over, Trinity walks past a man stuck upside down in a wall (from a kick delivered to him by Trinity during the fight). As Trinity walks by, the man falls to the ground and a wire can be seen attached to his neck for a split second before the shot cuts to him falling on the ground.
When Charra fires the rocket launcher for the first time there is smoke coming out of both tubes, while only one rocket is launched. When she fires the second rocket there are flames in both sockets, even though one is supposed to be empty.