It's night time when Lizzy and all the fairies leave to fly to London. However, when Lizzy flies above the clouds to get out of the rain, it's suddenly daylight again. As she descends down into London, it's back to night time. Also, the storm has past as she catches up to her father, and all the stars are out.
Mr. Twitches, the Griffiths family cat, is a calico cat. It is highly unlikely that a male cat can be a calico cat.
When Vidia closes the door of Lizzy's makeshift fairy house, her hair is suddenly completely dry.