Mars Attacks! (1996) - 6 major mistakes

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.

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

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.

Continuity: The helicopters at the landing site escort the saucer down, then immediately disappear. They are completely gone as the saucer touches down and do not participate in the ensuing battle, even though the Martians are never seen aiming their guns in the air.

Revealing: 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.

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.