During a foot chase through the rocks, Vincent takes a rest, setting his canteen down, but doesn't pick it up when he runs away. A few moments later he's holding the canteen and uses it to smack the face of an approaching alien.
At the humble desert ranch with the horse corral of the Mexican Americans, a roadway passes right in front of it - where the rancher's pick-up truck is parked. During the closing, that exterior view is shown from inside the house through the front door: that view is of an obviously painted backdrop of desert with cactus beyond a rickety pole railing, and no road next to the house, nor the edge of the attached high wood corral. In the next exterior shot of the ranch - the road, corral, and solid ground to roof pole supports are seen - not a rickety railing and desert sand with cactus.
Vikki's name appears with different spellings in different contexts. A sign outside the club where she works spells it "Vickie" while it is spelled "Vikki" on an interior sign. (One mitigating factor might be that the setting is bilingual with both Spanish- and English-speaking customers, but this would not adequately explain the discrepancies.)
Vincent walks toward the Hotel Popular and the cars that are parked outside of the building. Moments later, he is saved by Evans from being run down, but the cars outside the hotel are not the same.
When David and Vikki are driving out to the desert, they are driving at highway speeds in an open vehicle, yet Vikki's long hair stays perfectly still.
The alien ships seen in the show are all "reasonably" sized. As the alien ship takes off from behind the hill, the perspective is wrong as the ship appears to be immense, appearing to be far larger than objects in the foreground and on the near side of the hill.
During a fight with an alien, the alien drops his weapon. Mr. Vincent could have used this as evidence of their existence.
David Vincent is always trying to prove that the aliens exist. He knocks the disintegrator gun from the hand of one of them in the fight, but doesn't then think to retrieve it afterwards as easily convincing evidence since nothing like it exists on Earth.