In "High Hopes", the third episode, Owen Crawford examines the photo of an unidentified married couple abducted by aliens. The photo is of real-life couple Betty and Barney Hill, who became famous in the early 1970's when hypnotherapy sessions allegedly revealed that they had been abducted by aliens.
Matt Frewer (Chet Wakeman) appears on screen in six of the series' ten episodes, more than anyone else. Although Dakota Fanning (Allie Keys) narrates all ten episodes, she only appears on screen in the last four.
In the first episode character Sally Clarke gives the Alien "John" one of her lone star earrings to take with him back into space and she keeps the other. If you look closely in episode 2, when Russell Keys returns home for the first time in ten years, there is a Christmas star decoration behind character Bill, as he stands in the doorway telling Russell to go away, that is made to look exactly like the earrings.
The trivia item below may give away important plot points.
The fictional books, including the space comic book in episode 1 (from which the alien "John" steals his appearance) and the "Charlie Chestnut" book at the beginning of episode 2 which Jesse is reading before he's taken, have authors with the name of "Bohem", perhaps referring to real or imaginary relatives of the creator/writer of the mini-series.