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: 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: When the general passes the clipboard to the President to sign the nuclear release, the clipboard is actually upside-down.

Other: 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.

Continuity: When General Casey answers the phone en route to Pahrump, the helicopters following him drop back in an instant.

Revealing: 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.

Other: 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.