Other mistake: When the general passes the clipboard to the President to sign the nuclear release, the clipboard is actually upside-down.
Revealing mistake: After the Martian who is dressed up as a women spits a finger in the fish tank a bit of the Martian's mask near its mouth is torn away. As she chews the nitrogen gum the human lips move but her real teeth don't.
Deliberate mistake: At the end just before the president is killed he fixes his tie, but it keeps on getting fixed to messed, to fixed, etc. Deliberate homage to "A Few Good Men", but worth looking for nonetheless.
Continuity mistake: When the martians first visit earth in the desert you can see that the shadow from the poles at the red carpet is on the left side, a few seconds later after the silver ramp is unrolled and the martian ambassador walks down it and onto the red carpet you can see that the shadow of the poles is on the right side.
Other mistake: When those cute little Martians break into The White House and begin to blast away everything, a few of them get shot in the process. One gets shot in the helmet, and collapses to the ground, suffocating. A few minutes later, during the same scene, another gets shot, and likewise collapses. The animation of the two Martians collapsing is the same, just reversed.
Revealing mistake: When the two boys are playing the shooting game at home, they run away and drop the guns, yet the fish or whatever they are keep on getting blown up.
Revealing mistake: At the end of the film, when the singer holds out his arm and the hawk flies on to it, you can see the pad under his sleeve that would prevent the talons from clawing the actor's arm.
Continuity mistake: When the press secretary kisses the hand of the alien-dressed-as-a-seductive-woman, the eyeball ring is on her right middle finger but after she knocks him out (or kills him) the ring is on the finger between the middle and the pinkie. In subsequent scenes it's back on the middle finger.
Other mistake: In the scene where the President dies, after the General tells everyone to hush and there are agents/bodyguards slowly approaching the door, watch the door to the room before and while it explodes. There are lines in the door which mark the way in which the door will be blown open.
Other mistake: In the scene where they are at the church, the church looks tiny when compared to the car outside. When the camera shows inside the church it's much bigger.
Continuity mistake: The first time we see Tom Jones' backup dancers, they are about three feet apart. In the next shot, they are directly next to each other.