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.
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.
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.
Factual error: The scientists, having carefully charted their course to Earth, state that it is an 11 million mile trip from their planet. Not likely. Mars is our nearest planetary neighbor, and it's over 34 million miles away at its closest orbital approach. There are no planets any nearer to Earth than Mars. This is one of the very few cases where Rod Serling simply failed to do his astronomy homework.
Continuity mistake: When Mr. Ferguson is measuring the wax figures, he's shown holding a tape measure up against the figure of Landru (the one holding the rope). In the next shot, the figure is shown with no one near it. The next shot again shows Mr. Ferguson measuring the figure.