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.
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.
Continuity mistake: When Land is presenting to the investors during the invasion, a saucer flies behind him just as he puts on his hat. In the next shot, that saucer is gone, though there are others still in the background. It didn't move quickly enough to get offscreen in that time.