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.
The Circle Of Driving Again - S5-E8
Continuity mistake: After Adam crosses the railroad tracks in Grandpa's car, the next quick view through the front of the windshield to the back window of their car shows a street scene, and not the railroad crossing lights, gates, or tracks that should be there.
Uptown Boy - S10-E20
Factual error: Adam kicks the wheel chock from the pickup truck, and it starts to roll back. Based on the ease and speed of the truck rolling, the chock would have been firmly stuck against the tire and would not have moved when Adam kicked it.
Factual error: Occasionally one of the characters will make a key reference to some film or other cultural event that took place in 1989 or later. Like the neighbor stating she saw Ghost, which came out in 1990.
Factual error: Towards the end, Beverly is wearing Crocs. They only came out in 2002.
Factual error: Whilst Adam and Erika discuss their grandfather buying a timeshare in Florida Adam states that their Grandfather is 80 years old. Erika responds that he was born in 1903 - thus setting the episode in 1983. However Adam is wearing a "Queen A Kind of Magic" T-shirt - an album that wasn't released until 1986.
DannyDonnieJoeyJonJordan - S2-E10
Factual error: In this episode Adam and Barry are mocking Erica for being a fan of New Kids on the Block when she was younger - she must have gone off them pretty quickly as NKOTB only became well-known outside of Boston (their home city) on the release of their second album in 1988.
Factual error: Adam says it is January 27th, 1980-something, and he is watching the new movie "Cocoon", but the movie was released on June 21st, 1985, not in January.
Factual error: The Phillies were in the World series in 1980. Talk into remote controls did not come out till 1989. The party in the park the kids are dancing to the song "Tricky" by Run DMC which came out in 1986.
Suggested correction: The Phillies were in the 1983 World Series as well (which is the likely year as they lost), and the Goldbergs didn't have a talk in remote - the kids said they had just to wind up their father.