Continuity mistake: When Raymond arrives to check on Harmon, Flora is sitting at the breakfast bar opening the morning paper. She's holding it straight up in front of her, but when the shot reverses angles, the paper is suddenly lying flat on the bar.
Factual error: The astronauts land on an asteroid said to orbit a binary star 655 million miles from Earth. This is impossible, as that distance would place them well within our solar system. In fact, they'd be inside the orbit of Saturn, where of course there aren't (nor could there be) any extraneous suns. The nearest star to our system is, in fact, trillions (not millions) of miles away.
Revealing mistake: We see Redfield's car strike the invisible barrier from a side angle. It jerks to a stop and the hood flies up, but there's no other front end damage - until the angle shifts to a forward view, a shot of an identical car that had been previously wrecked. Now there's suddenly considerable damage to the front end, and the hood is in a different, much more crumpled position.
Continuity mistake: Rance McGrew's white horse is tied up with its head just a few inches from the hitching rail, but a moment later is untied and several feet away from the rail. Next shot, it's tied up close again, though no one's touched it. Finally, it's completely loose, and at the episode's end, is wandering into the street.