Factual error: In the scene where Neo is shot at by the French guy's henchmen, they shoot with different types of guns. 4 of these are submachine guns which would fire 9mm. Another is a M1928 Thompson would fire .45 APC. Lastly there is a Heckler and Koch G36K which would fire the drastically different 5.56x45mm NATO. When Neo stops the bullets, they are all 9mm Parabellum rounds.
Factual error: This happens throughout the entire film. Whenever bullet hits are shown on objects like cars or walls, the hits always appear to have been made from a weapon fired directly at the object - no matter what angle the shooter is actually firing from. This is particularly noticeable in the highway scenes. Bullet hits make very different impact scars/holes depending on the object and the angle.
Factual error: During the freeway chase scene, the albino twin appears in the back seat of Trinity's car next to the Keymaker. Morpheus points his gun at the twin and the twin whacks it out of his hand. The gun lands on the car's automatic transmission stick, and you can see the stick is locked in position "2", not in position "D" as would be normal for driving in any other condition than up or down a very steep slope at greatly reduced speed. There is no way Trinity could've run at the speed she appears to achieve on the freeway with her transmission locked into 2nd gear.
Factual error: In the freeway chase, when the agent tears off the car roof, it is seen as a floppy metal sheet. A roof is actually quite thick, supporting part of the car's structure, a built-in roll-cage, and of course the headlining. However, all of these things are nowhere to be seen.