Continuity: Whilst they are deciding how to raise the money, Number 4 - Kidnapping, or K.Nap - is there in one shot, then vanishes, then reappears with another option (Blackmail, or B.Mail) in number 5 that has not been there previously.
Factual errors: When Cheltenham Ladies College arrive on their school bus to play hockey, Cheltenham is spelt wrong on the side of the bus - spelt Chelteham
Continuity: The bank manager gives Miss Fritton four weeks to raise £500,000 to avoid the school being foreclosed. However, at the School Challenge final, Chelsea says she has been preparing for the show for six weeks, despite entering the competition only as part of a plan to get the money to avoid foreclosure.
Errors made by characters (possibly deliberate errors by the filmmakers): In the School Challenge final, the answer to the question "What is the volume of a sphere?" is given as pi r³, both by the show and the school bursar who says he's always been good at maths. He's not THAT good, as the volume of a sphere is actually 4/3 pi r³.