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.
Donna and Eric Sleepover - S2-E8
Continuity mistake: The design of Forman's Spider-Man sheets are of the Spider-Man from the late 1990's cartoon.
Continuity mistake: In the scene where Donna, Kelso, Eric, and Hyde are in The Hub after Eric Gets Suspended, Donna gets mad at the guys and leaves. But two shots later when Hyde is seen smiling and sipping his soda, you can see Donna's hair on the left side of the shot as if she was still sitting where she was before. (00:03:00)
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.
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.
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.
Moon Over Point Place (1) - S2-E26
Factual error: In one scene towards the end of the episode, Hyde is reading MAD Magazine in the Hub when Jackie interrupts him. He says he is in the middle of reading "Smokey and the Band-Aid," MAD's parody of "Smokey and the Bandit." However, the issue he has is June 1976, and the film was not released until May 1977.
Moon Over Point Place (1) - S2-E26
Continuity mistake: Red, Kitty and Midge are talking to Bob about Eric and Donna having sex. Red makes a point and Midge turns her head to look at Bob. The shot cuts and we see her from the side, repeating the head turn.
Answer: It's Ashton Kutcher's dog.