Factual error: No matter how sophisticated the STEM chip is, it would not enable Grey (Logan Marshall-Green) to go from a completely horizontal position to a completely vertical position in one fluid motion, without bending his knees, and he does this several times in the film.
Factual error: At the end, when the EMP explodes, the aliens are affected by the EMP but lights on the building and street lamps are still on. (01:19:35 - 01:20:15)
Continuity mistake: While racing through a parking complex to get to his daughter at the hospital, Lin ramps out of the exit and hits the font of his car on the ground leaving some damage, and even a part of the bumper hanging off. However in subsequent shots, the vehicle is undamaged. (00:02:50)