Continuity mistake: When Fred tells Wilma that he is stopping inventing at the end of the episode, he pours the remains of the reducing formula out of the window into Dino's bowl and Fred has a glass in his left hand. When he hears Dino at the front door, the glass has gone.
Continuity mistake: When Fred opens the back door and lets the dancing girls out of his house during Pebbles' Birthday Party, the door has a handle on the back of it. When one of the girls kicks down the door and lands on Fred a little later on, look at the door and the handle is missing.
Continuity mistake: Before Mr. Slate takes a picture of his employees, Sandy (the one that Fred gives a hot foot to) is standing by two other men. When Fred gives Sandy a hot foot, the men have disappeared, and when we see the photo that Mr. Slate has taken, they are back again.
Continuity mistake: When Barney is knocking on the door at Fred's house after seeing an advert in the newspaper, Fred says "I'll get it, Wilma!" and stops near the door. At this point, Fred is well away from the door, but in the next shot he is now standing near the corner of it.