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.
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.