Factual error: Eric makes a reference to "Sophie's Choice." This episode is set in 1978, but the book "Sophie's Choice" wasn't published until 1979, and the film adaptation wasn't released until 1982.
Burning Down the House - S2-E15
Factual error: Eric quotes "I'm not a doctor but I play one on TV." That quote was from a commercial in 1984.
Visible crew/equipment: As Donna plays footsie with Eric in the car while driving up to Jackie's ski lodge, a crew member's arm can be seen in the backseat. (00:05:17)
Revealing mistake: Hyde claims he's reading a Mad Magazine spoof of Smokey and The Bandit. Look closely at the issue, and he's actually reading a spoof of the movie Dog Day Afternoon. That and Mad Magazine didn't make any parody of Smokey and The Bandit.
Revealing mistake: When Fez and Suzy first meet, they do "12345 you owe me a coke" you can see Kelso mouthing the same line as well. (00:08:04)
Other mistake: Jackie comes out of her room while Fez has Caroline over, stating that she has to use the bathroom. However, in a previous episode, during Fez and Kelso's fight for the same room, it is the room that "has its own bathroom." (00:16:00)
Character mistake: When Bob shows up in the driveway with the free calendar from Red's muffler shop, the calendar says "Foreman and Son." Their last name is spelled "Forman" without the E.
Other mistake: How did Donna take the SATs with the rest of the group if she was going to a different school? She is even wearing her catholic school uniform.
Factual error: At the start of every episode we see the gang driving. Cars in the background are not from the 70s but the late 90s. For instance, the truck that comes up beside them at the end is a 90s Ford F150.
Continuity mistake: When Jackie leaves the basement and Lorie comes down she's wearing green pants, but as soon as she walks away they're blue jeans. The shirt, jacket are the same, but it's the pants that change.
Other mistake: When Bob comes to order from the clown, he gets told to go away since they're closed. He starts pulling away, but you can see he doesn't leave the frame quickly. The edge of the car is still visible when the gang is sneaking back over.
Oh, Baby We Got a Good Thing Goin' - S7-E18
Continuity mistake: When Kelso is trying to get the baby to not cry, you can tell Bob covers its face to the camera so we don't see that it's not actually crying. Cut to a different angle, and the blanket surrounding the baby has moved. Cut back, and the blanket is covering the baby again.
Continuity mistake: In the crowd scenes, Jackie comes back to her seat. A man sitting next to Donna looks at Jackie. The scene changes angles, and the man is looking straight.
Squeezebox - S6-E20
Continuity mistake: Kelso gets really close to Eric when he's trying to burn him about the other girl. The shot changes, and Kelso is further away.
We're Not Gonna Take It - S6-E6
Visible crew/equipment: The edge of the camera lens is visible throughout this episode. It's also known as vignetting.
We're Not Gonna Take It - S6-E6
Continuity mistake: When Eric is carrying the tray and they're trying to get him to drop it, he hops over a chair. The tray rotates between cuts. Look at the glasses.
Continuity mistake: The unibrow drawn on Jackie changes between the time we first and last see it. It's thicker the second time.
Visible crew/equipment: In the futuristic sequence, several times you can see the edge of the lens. This is likely because the show was reframed in 16:9 but on a 4:3 screen in 1999, the edge would not be visible.
Garage Sale - S2-E1
Continuity mistake: At the movies, Fez is daydreaming. Jackie's hand comes into frame as she's about to reach into his popcorn bucket. The shot cuts and her hands are at her side. She subsequently repeats the action.
Visible crew/equipment: When Kelso sees Jackie in the hallway at the rally, he walks over to her. As he does this, the shadow of the camera is visible on the lower half of his coat.
Answer: It's Ashton Kutcher's dog.