Factual error: Looking at a nuclear explosion that close will burn your retinas irreparably. One can be blind 30 miles away, just by seeing the flash. The little girl at the start is looking directly at the explosion when it hits, and continues to watch.
Lost/Found - S1-E1
Factual error: A mechanic is outside the ship repairing the shields. A fire starts, and the fire burns just as it would in an atmosphere. Impossible in the vacuum of space.
Episode #1.5 - S1-E5
Factual error: A VHS of the movie Indecent Proposal can be seen on the shelf in Dexter's bedroom. This episode takes place on 15 July 1992, but Indecent Proposal didn't release until 1993. (00:11:06)
Paul Is Dead - S1-E6
Factual error: The female British astronaut is in her space suit. There is a supposedly British flag on her left sleeve. But the flag is wrong. The red diagonal stripes are centered on the white field. They should be off-centered by 3/5 of the white space. Not centered. This is a common mistake you find in British flags bought outside the UK.
Episode #1.6 - S1-E6
Factual error: In Episode 6, Vincent comes out of his apartment building and before he reaches the curb, and has a chance to hail a cab, one is waiting for him. There was no ability to book a yellow cab in the 1980s.
Factual error: Barbara shoots her revolver at the guys chasing them. When she stops and gets out of the car, she opens the cylinder and we see she only has 1 round left. However, the other chambers should still have the empty casings in them instead of being empty.