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Continuity: When the spaceship is hovering overhead, we see various shots of the Maxwell family and others. In one shot we see the family from behind with a person in blue. We then jump to a shot from the front with that person not in picture. We then go to another behind shot and see the same person hurriedly moving into shot.
Factual error: When the world celebrates the Visitors' flight, there are scenes of joyous people from all around the world. Curiously, in each of these scenes it is daytime - even in Italy, China, and India, where it would be either night or dawn, given that L.A. time of the attacks is between 11 and 12 AM.
Continuity: When Diana is being chased by Donovan after crashing her craft, she has her normal human eyes. But during Donovan's strangulation attempt she has lizard eyes. As we saw in the original series, a Visitor's human eyes had to be removed by hand before the lizard eyes could be seen underneath.
Revealing: When Robert and Julie are attacked by snakes outside the cave, notice that in the shots when you see the backs of Robert and Julie there are hardly any snakes on the ground (I counted one) compared to other shots. The shots of Robert's leg as he sweeps the snakes away are almost certainly of a snake handler instead of the actor.