Continuity mistake: In the scene where Dr. Dawson and Olivia are seeking Basil's help at his house, Basil sits down and starts playing the violin, holding it in his right hand and having the bow in his left. When Basil the stands up in another shot, he is holding the violin in his left hand (like it's supposed to be) and the bow in his left.
Continuity mistake: When Professor Ratigan first climbs in his hot air balloon, it is a bright pink. Later, when Basil is chasing him through the sky in his home-made balloon, Ratigan's hot air balloon is a very dark burgundy.
Continuity mistake: During the scene where Professor Ratigan and Mr. Flavasham are in the dungeon, the robot pours the tea into the cup. During the next shot it completely vanishes. Then a couple of minutes later, the robot puts sugar into the cup where the tea was. The tea is still gone but it makes a sloshing sound.