When Flash comes to see what the girls are selling, the number plates on the car say GU06 SBX, but when he leaves the number plates read BN 0413. The new plates are German short time plates (registered in the city of Bonn) and they expired in April 2003.
When the teacher gets off the Cheltenham Ladies' College coach and talks with the minister, she says: "Between you and I..." No real CLC teacher would have perpetrated that glaring grammatical mistake.
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 with figures. The volume of a sphere is actually 4/3 pi r³. However the quote by the Bursar is a play on words as while he says 'figures' he's ogling the Spanish teacher.
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.
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.
When the girls first get off the bus and stampede through Trafalgar Square, we can see members of the public are being held back behind railings to keep them out of the girls path. They're also very obviously watching filming.
When Kelly suggests stealing the painting when the girls are brainstorming with Flash, the 'Posh Tottie' girls react by signing 'Oh my God'. However, the girl on the left makes the 'Oh' sign with her hand too early, and tries to hide her grin.
When the girls slowly walk up the National Gallery steps before the quiz final, we can see people in the background sitting on the fountains watching filming. Although it wouldn't be unlikely that a load of guys would watch intently as some attractive girls in short skirts walked by, There is also a line of peoples heads barely visible behind the top step. They're obviously being kept back to avoid disrupting filming.