Continuity mistake: At the polo field Brian is holding his teacup in his left hand. In the next shot of him it's in his right hand and in the next shot of him it's back in his left hand.
Continuity mistake: The students see a London bus approaching and run across the road to get on it. The approaching bus is a red RML-class AEC Routemaster with a grey stripe. The bus they actually get on, seen from the other side, is a shorter RM-class Routemaster. This one has a cream stripe and a gold London Transport fleetname.