Plot hole: The Alien family finds itself surrounded by armed cops, scientists, and helicopters yet the next time we see them, some seconds later, is walking around some deserted area. If the Government set them free there's no point in the chase of Mac. On the other hand, if the family managed to escape, then the scene with them defenseless in the supermarket is absurd. No explanation whatsoever is given to this really important part of the movie.
Plot hole: Mac tries to escape from the NASA premises reaching the closed electrified fence. In the next shot, couple seconds later, he has managed to appear on the other side, outside on the street. This is not possible since Mac electrocuted himself and burst like a balloon when he touched the fence.