Deliberate mistake: When the vortex is summoned to get rid of the monsters, other things get sucked into it. Cars, trees, light poles, other police officers. However other things or people who are more accessible do not get sucked in. For example, Phoebe hiding behind a bench, the bench itself, Phoebe's mother and a few cops hiding behind a cop car, etc.
Deliberate mistake: When the board member is shot up in the beginning by ED-209, in one or two shots you can see the bullet impacts happen about 1/2 a second after the shot starts (Criterion DVD version). (00:11:55)
Deliberate mistake: At the end of the film, two officers attempt to surround and handcuff Joshua. Using two officers to cuff someone is NEVER done for the exact reason of what ends up happening, as Joshua manages to grab a gun from one of the officers. Only one officer would have been doing the deed in the real world, but it's clear this error in being completely against police protocol had to happen so the good guys could prevail over the villain.