When Neo goes to work, the name of the company where he works is written on the outside of the building. It says: Metacortex. But in a later scene, inside the office, a banner says the name of the company is: Meta Cortechs.

When Neo first meets Morpheus, Morpheus's left arm is behind his back as he shakes hands with Neo. Then the scene changes and you see his left arm is straight. In the next scene it's bent behind his back again.

While Neo is firing rounds from the helicopter, notice the 'shells' falling from the weapon... they're still filled with live ammo.

When Neo fights with one of the men in black in the train tunnel, you can see the wires holding them up when they swirl through the air and jump backwards.

At the end of the movie, when Neo goes to answer the phone in the room, he gets shot by the agent. Then he falls back against the wall and leaves a blood stain on the wall. But if you look closely, you'll see the blood stain is on the wall before Neo even gets shot.