Adult Adam's narration states that the episode takes place on May 3rd. If you look closely at the TV Guide issue held up, you can see a November date.
The letter costs $0.22 in postage. The USPS didn't raise postage to $0.22 until 1985 but The Day After aired in 1983.
The intro states that it's May 3rd 1980-something just before they all watch "The Day After" (clearly the original broadcast since everyone is worked up about it). That TV movie originally aired on November 20th, 1983.
Adam shows his collection of Garbage Pail Kids collection to his girlfriend at the beginning of the episode. He has them in a binder which clearly says "shopTOPPS.com" which didn't exist in the 1980s.
In the episode, Erica smashes Adam's Teddy Grahams in retaliation for him sabotaging her chance of going to college in Atlanta. The episode is also centered around the TV movie "The Day After" being shown nationwide. The movie came out 1983, but Teddy Grahams didn't come out until 1988. But, this all this conforms the "it was 1980 something" premise.