A Chorus Lie - S3-E2
Factual error: A key plot point of this episode is the revelation of the Milli Vanilli lip-syncing scandal and that they didn't sing on their album, which happened in the fall of 1990, outside the 1980s setting of the series.
Suggested correction: The first public sign that the group was lip-syncing came on 21 July 1989, during a live performance on MTV at the Lake Compounce theme park in Bristol, Connecticut. As they performed, a hard drive issue caused the recording of the song "Girl You Know It's True" to jam and skip, repeatedly playing the partial line "Girl, you know it's..." through the speakers. "I knew right then and there, it was the beginning of the end for Milli Vanilli," recalled Pilatus of the incident.
The mistake didn't point it out, although the episode did, but the issue wasn't the fact that they lip-sync'd but the fact that they didn't actually do any singing. The minor incident you mentioned wasn't news that "shook the country." The news that it wasn't Milli Vanilli singing on their own album didn't come out until 1990.
My point exactly; while Milli Vanilli were revealed to be lip-syncing during a single live performance in the summer of 1989, it wasn't confirmed that they didn't sing at all on their debut album until November 1990.
Just Say No - S2-E20
Factual error: In a previous episode, Adam's uncle gives him a power glove and they talk about "The Wizard" which came out in 1989. A few episodes later, they talk about Reagan getting reelected, which happened in 1984.
Suggested correction: The series is constantly going back and forth through the 80s (Adult Adam always refers to the year in question as 1980 - something in his narration) - episodes are set in earlier times than previous ones.
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.