When writing to MacGyver, Peter writes on the envelope 725 Spooner Street. In later episodes, it is revealed that the Griffins live on 31 Spooner Street.
When Meg arrives home early in the show she immediately stands in front of an air conditioner. Minutes later it is learned that the winner of the dog show earns $500. Lois states that they can use the money to get the air conditioner fixed.
The hairdryer disappears after Brian puts it down on the sink in the bathroom.
When Brian is in the cell with the angry dog, the cell door's hinges swap sides.
The family has several fans running while watching TV, but when Peter opens the front door and enters, they all disappear.
Peter says he found Brian (that seems full-grown) out on the streets, although later on in the series there are flashbacks of Griffins getting Brian as a little puppy.