The man with the ponytail picks up the same magazine at the barbershop twice.
During the pet show segment, when the boy in the blue T-shirt puts his dog into position for the obedience test, he can be seen standing behind the dog. By the next shot, he's standing in front of the dog.
When Mr Bean talks to his teddy bear before leaving his car, he says he'll be back in about an hour (around three); this would mean leaving the car at two o'clock. Yet when he arrives at the pet show, the blackboard states that the show is due to start at one o'clock.
In the scene at the country fair, Mr Bean interrupts a boy doing the buzzer game. When Mr Bean is on his second go at this puzzle and stands up after unplugging the device, you can see the same boy come round a table behind Mr Bean. Cut to the next shot, the boy has moved across the back of the hall.
In the sketch with the train station, you can see a map of the British Isles; a piece of land shown in the English Channel doesn't exist in actuality.
The sign on the door of the train to Moscow uses a nonsense word (transliterated "Npultsa") to represent the Russian word for "Moscow" - the real Russian for Moscow is transliterated as "Moskva".