Continuity mistake: When Trinity confronts the agent on the rooftop and says, "Dodge this", she points her gun to temple of the agent while his head is turned to her. He glances back, but never fully turns his head. The instant next shot shows him being shot facing Trinity with the gun in the middle of his forehead. (01:42:20)
Continuity mistake: In the beginning of the movie, where Trinity runs from the agents, she jumps towards a window. She turns slowly in the air, eventually facing upwards when she crashes through the window, no longer turning. From the inside shot, however, she comes through it face down (so she can roll forwards down the stairs). (00:04:55)
Other mistake: They are presumably in the US - trying to make it look that way, anyway. Cars driving on the right, speaking English etc. However the filming location was overseas, revealed by the elevator in the lobby scene. When they hit the button, the plate refers to the elevator as a lift.