Other mistake: When Neo is being chased by the three agents through the outdoor marketplace, pay attention to the shot of the guy being picked up by an agent and flung through the air. There is a woman wearing a red sweater to to the slight left of the agent. She does not flinch, even though the guy in front of her has just been thrown 15 feet into the air and into a produce stand. She just stops for a second to let the guy fly past her, and she then simply resumes her walk. Other people around her react... (01:54:40)
Other mistake: When Morpheus makes his escape, Agent Smith shoots through the walls with a noticeable time between shots. However when you see the bullets in motion (the 'bullet time' sequence), they're so close together in time that Morpheus doesn't appear to move in the interval between shots. Even if these are supposed to be later shots they could not be fired so close together either by the agents or by the guns used. The first two bullets are some distance behind Morpheus, corresponding to the change of direction of the shots fired by agent Smith to track Morpheus' movement - this also doesn't fit with the shots seen in the 'bullet time' sequence.
Other mistake: When Neo shoots with the chopper's machine gun the window smashes from a single point in the middle, shattering two panes. Water then starts splashing up from bullet impacts right at the base of the window, but the glass doesn't smash anywhere around there - it could only work like that if Neo was shooting down at an incredibly sharp angle, which he obviously isn't. (01:43:20)
Other mistake: In the bullet-time sequence in the subway station the lighting on Neo and Agent Smith doesn't change even as they spin round each other, principally because they were in a green screen chamber with even lighting to shoot the movie. It sticks out because the lighting on the CGI set (for the bullet-time shot) is pretty dim with light in specific areas. (01:50:10)
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.