The front door of the set has a brass mail slot, but exterior shots are of a door with no slot.
In Season 1 Nell's mother's name is Emma Harper in later seasons her mother's name is Maybelle Harper.
One of the opening credits scenes shows Neil accidentally putting a vacuum hose into a fish tank and sucking out all of the water. Any 1980s vacuum cleaner would have immediately shorted out if water was sucked into the intake.