In one episode, Red is shown at the kitchen table opening mail. He removes a credit card mailer, and the credit card clearly has a hologram on its face. Holograms were not used on credit cards until 1983.
A large number of the other props and products used on the show are not consistent with the period (flip-top drinks cans, barcodes on toys, etc, etc) or are not represented accurately (Betamax VCRs that could record too much material on one tape, etc).
In the pilot episode all Coca Cola bottles have a red printed label stuck to them. However Coca Cola didn't had printed labels in 1976, they had full-glass bottles with the Coca Cola molded in the glass. In all later episodes, the correct bottles are used.
In the opening scene of the premiere episode, the boys are looking at a Playboy centerfold, circa 1976. However, the magazine is perfect bound, not saddle stitched (stapled) as Playboys were at that time.
In the January 14 2003 episode, Eric holds up Star Wars action figures for Red to identify. The figures he holds up are not the straight-armed figures from the 1970s, but are the posed figures from the 1990s. The episode takes place in 1979.
In one episode, someone notes that a character's father "works for Six Flags." The park now called "Six Flags Great America" north of Chicago and south of Milwaukee was owned by Marriott and called "Marriott's Great America" until 1984 when Six Flags purchased it. And everyone called it "Great America" anyway.
Donna justifies taking Kelso's van by reminding Eric that Kelso melted his G.I.Joe figure. Eric says, "The Real American Hero deserves better." G.I. Joe wasn't called "A Real American Hero" until the 1982 re-launch.
Whenever Eric's last name is shown on a transition in the beginning of a show, his last name is Spelled "Forman". In episode 7-10, on the calendars Red has printed for his muffler shop, Forman is spelled "Foreman".
In the episode "The Drive-In" when Fez's foster parents are afraid that he is listening to rock-devil music, Hyde shows him how to hide the rock records in soft music record holders. He demonstrates with a record he claims is Alice Cooper and a Pat Boone holder. While the Pat Boone holder is correct, the record he is holding is actually a Led Zeppelin record titled "Led Zeppelin 4".
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 the Season 1 episode "Eric's Burger Job"' Donna's sister Tina Pinciotti is introduced. While the character was written out immediately after this episode, the actress playing Tina frequently appears as an extra in the background of many scenes throughout the first few seasons- she is easily spotted by her round blonde haircut.
In the episode where Fez and Jackie fight because he turned her down: Fez puts green dye in her shampoo. When she steps out of the bathroom to yell at him, you will notice that a safety pin holding up her towel appears and disappears between shots.