Visible crew/equipment: Before the church scene, Mr. Bean drives into the car-park and knocks the blue car off the road. Look at the car closest to the camera, as Mr. Bean reverses, you can see a person and a crane above him reflected in the window. Also, in the blue car's window closest to the camera, you can see dolly tracks.
Visible crew/equipment: When Mr Bean parks his car outside the examination hall, as he reverses into his spot, you can see a group of plain-clothed crew members pushing the camera reflected in the car nearest to the camera. More noticeable as the camera is actually moving.
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.
Visible crew/equipment: In the scene where Mr. Bean takes the sign for the bus stop, he drives away with another person. As the camera turns, you can see the cameraman in a yellow jacket ducking down in the bottom of the back window. Also, you can see an old man in a hat watching the filming, he is over by the tree reflected in the window.
Revealing mistake: When Mr Bean's book falls apart, he tries putting the book back together, and he holds one page up to the camera and it has a slight reflection as if it is glossy paper. As far as I know old books like the one Mr Bean had don't have pages like that. It's an obviously fake book.