When Patrick Ross is raping the girl in the supermarket parking lot, she drops her purse just outside the rear door of the black van, he does not pick it up. A moment later when Col. Burges and Press arrive at the same van, the purse is gone.
In the nursery near the end, when Patrick's son extends the tentacles and rises to the ceiling, from the first view just behind of and slightly to the right of Patrick, the boy starts out several feet away from in front of Patrick, but when the view switches to overhead the boy is rising from a spot less than a foot from in front of Patrick, practically touching him.
When Eve is escaping her holding area, the female guard going for the alarm has her hair done in a ponytail. For obvious reasons, women in the military are required to have their hair in buns if it's over a certain length.
Once they complete their mission to Mars, the astronauts receive a video message from the U.S. President. Later on in the film, when Colonel Carter Burgess Jr. reveals to Senator Judson Ross that Patrick Ross is involved in series of murders, a picture of the actual U.S. President at the time (Bill Clinton) can be seen hanging from the wall in the office. Several months have passed between the Presidents Video message and Colonel Carter Burgess visit to Senator Judson Ross. (Round trip to mars was 18 months.) Enough time for a presidential election to have take place
In the stock footage of the space shuttle landing, the name "Discovery" and the NASA logo are visible on the shuttle's side (rather than the fictional name "Excursion" and fictional space agency N.S.E.G.).
The goof items below may give away important plot points.
When he is carrying the stripper into the woods he had no blood on his face. When he is stomping the ground he has blood on both cheeks. When takes his child into the building the blood on his left cheek has changed shape and is lower down than before.
When Patrick kills his father, one of the tentacles goes though the front of his neck, directly in the middle. The father is screaming the entire time, and continues after the damage to his neck... the screaming should have stopped or been a harsh rasp as the damage was very clearly to the trachea and larynx.