Continuity mistake: When Mr Bean talks to his teddy bear before leaving his car, he says he'll be back in about an hour, at around 3. This would mean he's leaving the car at 2. But later, he arrives for the start of the pet show, which the blackboard states was due to start at 1.
Continuity mistake: 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 disappeared from where he should be behind Mr Bean and can now be seen walking across the back of the hall.
Continuity mistake: At the country fair and during the pet show segment, when the boy in the blue T-shirt is putting his dog into position for the obedience test, he can be seen standing behind the dog as we look at it, but on the next camera cut, he's standing in front of the dog.