When the Jennings' daughter Paige looks at a postcard sent by her mother while she was away, the date on the postmark is 1982 (the current year the show is set). However, the postcard has as Liberty Bell Forever Stamp on it, which was not released until 2008.
(at around 16 mins) An aerial shot shows the U.S.S. Harry S. Truman (CVN-75) and an unidentified Wasp-class amphibious assault ship in dock. While the episode is set in 1982, the Harry S. Truman was not commissioned until 1998 and the Wasp-class did not enter service 1989.
When Paige uses the telephone to make a call, she holds it in both hands and dials with her thumbs, the way people text on mobile phones today. It is highly unlikely a person would have dialed that way in 1982.