Visible crew/equipment: After the cat hisses at the children and Miss Price says they startled him, the cat is shown moaning and you can see a shadow moving across its head. It's not Miss Price, as she is up on the stairs, and it's not the children, as they are not close enough and are trying to keep their distance as they move towards the stairs. This is likely a crew member moving toward the cat in order to get it to react. (00:10:10)
Revealing mistake: After Lansbury makes her clothes start to move, her nightgown attacks someone and you can notice the strings that make the gown move.
Plot hole: When Miss Price, Professor Browne and the children return from their magical journey to the island of Naboombu and realize they no longer have the Star of Astroroth pendant, Miss Price says, "I should have known it would be quite impossible to take an object from one world into another." Yet, they had no problem taking themselves, the bed, blankets and pillows from one world into another.
Character mistake: The closing shot of a newspaper article shows the word "rumor", film is set in England where it's spelled "rumour".