When Gielgud shows Mary the secret passage through the mirror, he repeatedly touches the glass without leaving any fingerprints although the glass is covered in dust and Mary did leave fingerprints when touching it in an earlier scene.
As Uncle Albert sings the song about the pebble to Father and Mother in the study and the camera moves back and forth the ink smudge on Father's right ring finger changes in size and colour.
When the Rat Queen bites the Rat King's ear as a punishment for being whiny, he stumbles away from her, pressing a hand to his ear and crying "You bit me!", looking very pained. However, when the Rat Queen stops yelling at him, you can still see him standing in the same position and with the same pained expression, but in the next shot (a second later), he's standing in a quite normal position, looking angry rather than pained.