A Kick-Ass Risky Business Party - S3-E1
Other mistake: Barry and Erica are watching Lany band with Beverly. They are hiding behind a bookshelf of board games. One of the board games is Showdown Yahtzee. This game did not come out until 1991.
O Captain! My Captain! - S4-E11
Other mistake: Barry climbs up on the desk and comically recites the "Oh Captain my Captain" refrain, which is in reference to the finale of Dead Poet's Society, which came out in 1989. An actual time jump forward, that would make him 20-something, which he isn't. And makes no sense for the episode, which is still set in the mid-80s.
Yippee Ki Yay Melon Farmer - S6-E10
Other mistake: In this episode, Adam watches Die Hard for the first time. Earlier in season 2-1, he is shown wanting to watch Die Hard. Die Hard wasn't released until 1988 and the Goldbergs would have at least had 3 Hanukkahs before this episode. This is impossible considering the time frame at to be watching it at both times.
