Revealing mistake: When Neville gets back to his fortress-apartment, he boots up the video surveillance system, switching on several closed-circuit monitors. The very largest screen, however, shows himself, looking toward the screen. As he turns about his image on the screen doesn't turn the correct way; it moves like a mirrored image: he turns to the right, the image turns to the left. The image ought to turn in the same direction. The image in the video screen was photographed separately (and not quite inaccurately), and added later in post-production.
Revealing mistake: Watch when Dutch throws the flash grenades during the stadium scene. When seen igniting on the ground, they are positioned closely behind large boxes and other bulky debris, to hide the special effects used to create the light. It would be virtually impossible to toss the grenades any distance and then have them drop down into place so perfectly on the far side of the conveniently placed obstacles.