Continuity mistake: In class when the agent tells the President the aliens are attacking and the President responds "You mean, right now all of these children's parents could be dead?", there are some items on the table next to the President. When it cuts the items has changed position.
Continuity mistake: When Tom (Charlie Sheen) is about to pick up the picture, you can see that the person on the right on the picture is on the far right of the frame. When it cuts to a close-up of the picture the person on the right has moved to the middle of the picture. In fact it's basically a different picture.
Continuity mistake: In the shots when the Saw Villain is speaking to Shaq and Dr.Phil, we can see the two toilets right next to Shaq. Throughout the entire speach the toilet on the left has its lid down and the one on the right has its lid up. When Shaq shouts "Oh my God, how are we gonna get outta here", the toilet on the left has its lid up, and the one on the right has its lid down.
Continuity mistake: During the Village parody scene with the man with the knife in his heart, Cindy leans over and talks to him and winds up pushing the knife completely into his chest by leaning on him so that no metal part is visible. In the next shot, the knife is back as in its original position.