Continuity mistake: In the sketch where Mr Bean drives to the dentist, there is a part where he starts to dress himself. If you look out of the window, the scenery keeps changing dramatically. In some shots he is driving along a single lane carriageway with buildings on the sides and in other shots he his driving along a dual carriageway with no buildings on the sides, all while he is getting dressed.
Continuity mistake: When Mr. Bean is dressing in his car on the way to the dentist, just after he puts his shirt on the camera cuts to show him from the rear of the car. In this shot he has his dress pants on already, but he hadn't put them on yet and in subsequent shots they are gone again.
Deliberate mistake: When Bean is putting on his socks as he is driving, his foot presses the horn in the centre of the steering wheel. Except that the horn control is actually on the right-hand column stalk (you can see the horn symbol on it). This was most likely an added comical sound effect.