Everyone wonders about Donna's sister, Tina, who only appeared in one episode. But, Midge references a second daughter, Valerie, who went off to college and was never shown or referenced again.
At the very beginning of the show, you can hear the theme song of the show the kids are watching. Then, after a few seconds, the theme stops and you hear nothing else from the TV.
During Kitty's birthday fantasy, Eric's wristwatch vanishes and reappears between shots.
At the party, when Kelso sprints to talk to Eric's sister, he knocks over the lamp. In the next shot, when they are talking about the gifts, the lamp is back where it was, without any damage.
When Jackie goes into the living room to tell Eric that Donna is waiting for him, the microphone is slightly visible.
When Eric opens his present of an 8-track player, the scene is shot from the ground up, facing Eric. High up, behind him, you can see the top of the living room set wall and briefly a round studio/stage light.
When Eric is sitting alone in the basement, a moving shadow can be seen on the wall above him.