During the other father's song, notice the red record player by the door and the position it's in, with the lid facing Coraline when he says, "making up a song". When the camera angle changes and he says, "she's a doll", the record player's position changes completely, with the lid now facing the wall.
When the other mother is making Coraline an omelet, pay attention. The egg yolk is in the shape of Jack Skellington's face. This is a reference to The Nightmare Before Christmas, another film directed by Henry Selick.