Plot hole: In the Upper Class Twit of the Year Show, there are five contestants. However, after Oliver runs himself over, in the events that follow there are only four props for the remaining twits (four mannequins, rabbits, and guns); since Oliver's death was unforeseen, shouldn't there be five of each? (This mistake, by the way, is rectified in the film version of this sketch).
Plot hole: Lots of factors here: The doctors end up with the opposite kids that they were supposed to have... Why didn't they simply switch in the first place rather than go through all the drama? Also, the male doctor admits Alice let him in and most likely Alice would have told him first door on the right (like she's given directions in other episodes) to locate Peter. And the biggest question of all is, what doctor would make a house call and not look for their patient rather than just ending up with someone else they were not called to see (remember, each parent called their own doctor to see their biological kid).