At the scene when grandma debates her alcohol problems, you see the little kid resting on the table. The guy moves the cam to the left, and than suddenly the little girl is being hold by her mother a few feet away.
Ice starts pouring out of the fridge when the aliens cause things in the house to go haywire. The ice is not there a few minutes later. There is also no reference to anyone cleaning it up or slipping on its water later on (it would have melted on the kitchen floor within a few minutes).
When the camera's battery is low, a "Low Batt" message flashes on screen. This would only be visible to whoever was recording and would not appear on the recorded video.
When somebody shot the alien with a sawnoff shotgun inside of a hallway, you can obviously tell that there was a cap in the gun. If the gun was real, then there would be a loud blast that would be louder than the gun cap.
When Tommy is told to go back into the house while Kurt and his brother Brian go investigate the loud bang, Tommy is then seen saying "guys wait up" from a distance, he runs and his voice gets much more clear to the camera, despite the camera being right behind Kurt and Brian the entire time.
When the camera-man puts on the lights on his camera, the whole room lit up. No old cameras would have this powerful lights, which indicates that the light-source came from a spotlight or something else and not the camera itself.
The entire film blanks out cursing words, however Kurt says "come on you b*****" when they lock him in a room.