Continuity mistake: In the Oracle's house there is something wrong with the glasses in the cupboard behind Neo. When he's looking at the children, there are three small glasses in front, a big one behind and something else beside them. In a shot from below when the boy hands the spoon to Neo, the big glass has now moved to the left of the small ones. (01:08:25)
Continuity mistake: When Trinity leaves the matrix at the start through the phone booth, the garbage truck driven by the agents rams the phone booth and punches a big hole in the brick wall. When the truck reverses there is no visible damage to the truck, not even a broken headlight, even though it has just crushed a phone booth and a brick wall. (00:05:40)
Continuity mistake: Near the end when Neo runs and jumps into Agent Smith's body, the other two agents are shown standing at the end of the hallway. If you look closely at the shot of the agents after Agent Smith explodes, the tie clip of the agent on the left side of the screen is angled diagonally across his tie. Neo flexes the walls, and in the next shot of the agents the tie clip has returned to where it should be - horizontally across the tie. (02:01:20)
Continuity mistake: As Neo awakens inside his "goo tube", a few from overheard shows him raising his arms against the covering of his tank. The shot changes to one from the front and suddenly Neo is in a sitting position and raising his arms up as he breaks the covering. When Neo was first raising his arms, he was laying on his back. (00:31:15)
Character mistake: When Morpheus is explaining to Neo the reason the Matrix exists, he states that a human being gives off 25,000 BTUs of body heat to help power it - this is just not true. Even human beings that are running a marathon can't give off that much heat, and the humans in the Matrix are all lying down, not moving.