Other mistake: When Ray pulls up to Mary Ann's home, the front exterior layout and dimensions of the house are evident, from its near center front door to the two car garage, in front of Ray's van. The side exterior wall contains two large garage doors, which are about 35-40 ft from the location of the front door, with no small basement windows at ground level; inside, beside the front door, the stairs that lead to the basement run parallel just under the stairs in the foyer. In the basement, the small windows on the far end of the furnace room they run into are only about 20 ft from the basement stairs. Not only are the small windows non-existent in the exterior shot, but it's entirely impossible for two small windows to be where they are, considering the exterior footage of the house.
Other mistake: In the scene where the aliens appear to throw the Bayonne Bridge off its pylons and the eighteen-wheeler crashes on top of the apartments, look closely on the far right. There is a red car, and right above it is a round black object above the hedge. As the scene continues, it starts to fade away into the red house behind it.
Other mistake: When Dakota Fanning and Tom Cruise are in the house being searched by the alien probe, they use a mirror to shield themselves. We can see a diverging beam of light coming off of the probe, and therefore we should be able to see a related beam coming off of the mirror, widening even further. No second beam is visible.
Other mistake: Mary Ann and Tim's basement, and Ogilvy's cellar are the same set, just dressed differently; note the positioning of the windows, the stairs, even the little room off to the side. Also, some items in both the basement and cellar are the same, for instance the chair. While they are in the basement and the plane is crashing, before they run into the side room, Ray grabs his gun off of that chair and later in the movie when they are in Ogilvy's basement, Rachel is in that chair when the aliens are in the cellar.