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. (00:02:15 - 00:04:00)
Revealing mistake: Throughout the episode, the "frozen" people can be seen breathing and moving slightly. This is particularly apparent in the beauty contest tableau.
Revealing mistake: As Peter goes to the fishers, the pair shown on the bridge behind him are obviously photographs.
Character mistake: The "frozen" woman on the stairs during the welcome mayor scene repeatedly blinks her eyes.
