Other mistake: Taylor believes he is on a planet 300 light-years from earth for most of the movie. However, after spending months there, he would have seen the moon at night a number of times, letting him know where he really was before seeing the Statue of Liberty.
Other mistake: After running from the falling boulder in the forbidden zone, Dodge walks ahead of Taylor and Landon. In one shot, Dodge is shown in the distance, but you can two tracks in the dirt between him and the others. (00:19:50)
Revealing mistake: In the scene where Taylor is running after the humans when their clothes are stolen, they're supposedly naked. As Taylor is running through the trees, you can see he is wearing flesh coloured shorts. (00:28:45)