Gulli, Gulli and Beti
While Vetinari and Colon are conventionally dressed (by the standards of Ur), "Beti" has to adopt the gauzy, filmy, dress designed for a woman about a foot taller, and with far more to conceal which other people might actually like to see.
It is a tribute to the sheer strength of the Laws concerning Narrative Causality, that they fight such a spirited rearguard action that Nobby is actually mistaken for a woman. Especially by other women who at first feel sorry for such an unfavoured lady, but who then respect and appreciate "her" liberated streak and unrestrained sense of humour. Nobby may have done more to awaken a womens' rights movement in Klatch than is apparent...
Meanwhile, Colon is playing the part of a fat, slow-witted fall guy to perfection, and the Patrician is also letting himself go on holiday from his usual cares by performing routines which are straight out of the Guild of Conjurors training manual. (only better)
They also perform a shuffling Djelibeybian sand dance, and succeed in getting a donkey down from a minaret without anything having to make a distressing splash in the sand. Finally, they hijack a magic carpet.
The Roundworld act being parodied here are the British music hall entertainers Wilson, Keppel and Betty  , who entertained the nation between the 1920s and 1960s with a performance in ill-fiting burnous and fez (for the men) and something gauzy and filmy with strategically located soup-plates (for Betty) which contained most of the above elements, save perhaps for the donkey and the magic carpet. They are perhaps remembered for the Egyptian sand dance : this has inspired two chart hits, the Bangles' Walk Like an Egyptian , and Jonathan Richman's band The Modern Lovers released an updated version of W,K & B's signature "Sand Dance" theme under the title of Egyptian Reggae.... 
The act is also partially based on comic and magician Tommy Cooper. Whilst demonstrating "Find the Lady" Vetinari's use of the line, "Egg, Melon. Melon, Egg" is a reference to Tommy's "Bottle, Glass. Glass, Bottle" catchphrase while badly performing a magic trick. Tommy's act and stage persona, he performed simple magic tricks and wore a fez, were derived from the itinerant street magicians found in arab ports like Alexandria and Port Said known as Gully Gully Men.