At about 47:00 when Spain crawls away from the alien, you can see hand prints from previous takes.
During the last scene where the creature goes after Spain, a string can be seen attached to it (aprox 49 mins).
When Luis Spain takes Mrs. Clarke to a doctor's appointment, they drive through the country. The Clarkes are supposed to live in Chevy Chase, Maryland, a residential suburb located adjacent to Washington, DC, several miles from open country.
Oliver Fair finds Luis Spain's abandoned car in a mud patch and desperately wonders which way Spain went - never once checking the muddy ground to see which direction his footprints indicate.
Gov. Hillerman talks about the birth of the aliens, saying it happened a billion, billion years ago. The universe itself is not quite 14 billion years old, making that impossible.