When Neo is at work in his supervisor's office getting yelled at, notice the window washers. When the camera shoots from the outside of the building, look at the soap on the window.. it strangely resembles the Matrix pattern as displayed on a computer screen. Also take notice of the look of confusion on Neo's face - like he had seen that pattern somewhere before. See more...
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The Matrix (1999) - 19 visible crew/equipment errors
In the scene where Neo and Morpheus are in the training program with the girl in the red dress, after Morpheus has paused the program you an see a camera and a black fabric cover around it reflected off Morpheus' sunglasses for a considerable amount of time. Noticeably in the shot considerably close to his face while talking.