Visible crew/equipment: As Jackie opens the door and comes into the room near the end, you can see the bottom of a microphone. (00:20:15)
Continuity mistake: When Fez knocks the clown over and shatters it, you see the head roll in front of the body and out of frame with the nose still attached. Donna then turns around and runs in to take the nose from behind the body of the clown.
Visible crew/equipment: Stage lights and the end of the set can be seen in the scene when Kelso is confronting another man for courting Jackie. (00:16:00)
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.
Factual error: Eric has diecast model cars in his bedroom; those were not around then. The ones he has weren't available until the 1990s.
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.
Character mistake: Right after Hyde comes into the kitchen to get whipped cream for the stripper wife, Kitty Forman says "Kurt" instead of Red to Kurtwood Smith.
Suggested correction: She says, "Okay, what were you two talking about?". She doesn't use any name at all.
Character mistake: As the little boys are trying to get a peek at Donna's breasts, you see more and more of them. The first two times, you can't see them. The final time, you can see a kid or two far left. They're having trouble standing still. When it cuts to a wider shot, the kids come from behind the wall to see Donna. Chances are, since the aspect ratio was intended for 4:3 TVs, they didn't intend for the kids to be visible.
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.