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.
Laika had to hire a professional to sew the clothing for the puppets. Why? Because the knitting needle was as thin as human hair.