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: 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.