In the Show, Eric turns 17 years old in 1976, placing his birthday in 1959. However, the crew doesn't graduate High School apparently until 1979, placing all of the characters at 20 years old at time of graduation
In some episodes, characters use an insulting term, dillhole. However, the term dillhole was coined on the TV series Beavis and Butthead during the 90's.
The gang go to a WWF wrestling show in Milwaukee in the late 1970's. The WWF didn't start running Milwaukee until 1984. In the 1970's Milwaukee was one of the AWA's main cities as WWF television wasn't seen in the Milwaukee market until 1984. Technically if the gang were really wrestling fans at the time, they would have been AWA fans instead.
Throughout out the series (esp. during the last seasons), it's clear that most of the actors/actresses portraying teenagers are actually in their 20s+. This is done as to not interfere with the schooling of real teenagers and to give the general viewing audience who are teenagers (or young people) themselves someone they can look up to.
In a few episodes the cast talk about going to Six Flags. Since they live in Wisconsin they would be referring to Six Flags Great America in Gurnee, IL. However it was Marriott's Great America not Six Flags through 1983.
In most of the scenes, especially the outside scenes. The set lights can are reflected in Hyde's sunglasses.
It would be possible for the Forman's address to be 416 Marie Drive with the Pinciotti's at 853 Marie Drive and still be next-door neighbors, if it was the result of a street expansion.
In the opening credits, you can clearly see many modern cars. The most obvious is a '97-'02 Ford Expedition that passes the cast on the passenger side.
The poster showing world flags in Eric's room has some flags of countries that didn't exist in the 70s (e.g. Estonia and Georgia).
Several times in the series when donuts are present, they are in a Krispy Kreme box, but Krispy Kreme donuts did not come to Wisconsin until the 2000's.
Throughout the series in the Forman's kitchen there are modern boxes of Frosted Flakes as well as Reeces Peanut Butter Cup cereal. Reeces Cereal wasn't invented until the mid 1990's.
In some episodes, cassettes are shown with clear housings - which weren't introduced until 1984.
As with many TV series, the ages (or birthdays) of the characters are inconsistent with the time setting.