Factual error: When Neo is shooting thousands of bullets out of the Gatling Minigun from the helicopter, there is a shot of "cases" and links falling from the machine gun onto the helicopter floor. Only those "cases" are complete rounds, bullet and all (or possibly blanks) instead of just empty, spent cases.
Factual error: During the lobby shootout, Neo pulls out a pair of VZ-61 Skorpion machine pistols and runs down the lobby blowing away the guards. While he is running, we see the blank shells falling to the ground beneath him. However, the shells are 5.56mm NATO, which is a cartridge that is too long to fit in this gun.
Factual error: When Agent Brown shoots at Neo on the skyscraper, the last shot scrapes Neo in the knee and on his shoulder. This would cause both shots to be vertical when standing up. However, when Neo stands up and indicates to the scrape, the shoulder scrape is horizontal - not possible given the trajectory Agent Brown is firing from.
Factual error: In the "Deja Vu" sequence, when Mouse opens the box containing his Auto Shotguns, they are stored with a few belts of .50-caliber BMG ammunition, which would be useless in a shotgun. Also, despite firing about 20 or more 12-gauge shotgun blasts at the SWATs, he fails to hit anyone, even though that equates to about 240 flying lead pellets.
Factual error: When Neo was getting shot outside room 303, Smith fires 10 rounds into him. More if you count every time Neo is shaking in the seat as additional shots. The Desert Eagles in the movie are chambered for .50 AE. You can tell this because the barrel isn't fluted. This means it has a 7 round magazine. Agent Smith runs out of ammo in the subway, so it's not like he can hack his gun because of his software.