Other mistake: In the scene where Trinity tries to deactivate alarms in the building she types "disable grid nodes 21-48". Then a warning appears on the screen of her laptop which says: 'Disabling nodes 21-48 will disconnect sector 11 (27 nodes)'. However, because of the fact that nodes 21 and 48 are both included in the range, the total number of nodes to be deactivated is 28 (not 27 as written on the screen). (01:43:50)
Other mistake: In the freeway scene, when an agent takes over the black truck, he turns around to go the other way. As he does this, there is a shot from the side of the truck as he turns. In this shot you can see that the front of the truck will easily crash into the wall, but cuts away before it does.
Visible crew/equipment: During the scene where Neo is talking to Agent Smith in the park area where Neo was talking to the Oracle, there is a close-up on Agent Smith's face. In his sunglasses you can see a bright white screen to reflect the light onto the faces of the actors. This isn't visible in any non-reflected angles. You can also see the cameraman on the other side. (00:51:15)