When Barry is calculating the time he should wait before calling in to win the radio contest, he shows Adam the calculator screen and says "37 minutes", but the screen is blank. A moment later when the camera cuts back to Barry, there is a digit on the screen, but it is not 37.
A poster hanging in Barry's room purports to depict Philadelphia's Veteran's Stadium--home of the Phillies--but actually features Washington's RFK Stadium instead.
When Erica's Band, The Tangles are playing their "original" song, the narrator, adult Adam, states that the song was written by Joan Jett. Although "I love Rock n Roll" was recorded by Joan Jett, it was a cover song written by Alan Merrill of the Arrows. Not a goof: Voiceover Adam actually says it was "a little song sung by Joan Jett" and "it was already a Joan Jett song." He never says that she wrote it.
Although the show is set in the 80s, when Barry throws out the first pitch at the Phillies' game, he is at Citizens Bank Park, the current home of the Phillies, which did not open until 2004.