Two episodes prior (Dinner Party (1999)) while planning the dinner guest list, Frasier (Kelsey Grammer), being out of blackballs, throws a fig into the blackball bowl at Niles's (David Hyde Pierce) suggesting the Cromwells as potential guests. Niles objects, saying, "That's just a dried up old fig." To which Frasier responds, "So's Missy Cromwell." In tonight's episode, Missy Cromwell has apparently bid on the spa day of beauty, prompting Frasier to observe that her last day of beauty was sometime during the Johnson administration.
Frasier's IQ of 129 would be classified as "very high" and would mean that he has a higher IQ than roughly 98% of people within his age group (IQ is always measured relative to other people of similar age). Niles' IQ of 156 would be classified as "extremely high" and would mean that he has a higher IQ than roughly 99,99% of people within his age group. In this episode the brothers are bidding for a diner with geniuses. While there is no scientific definition of a genius, in colloquial terms Niles could be considered a genius, which Frasier acknowledges at one point.
According to the IQ tests taken when they were children, the brothers learn that Frasier's (Kelsey Grammer) IQ is 129 and Niles' (David Hyde Pierce) IQ is 156.
In the end scene over the credits, Martin is barbecuing on the balcony with QEII, in full court robes and crown, obviously having the time of her life. Quick cut back to the inside of the apartment, Daphne wakes up with a start, apparently just having had an Englishwoman's nightmare.
Despite the large difference in Niles' IQ over Frasier's, he exhibits such extreme naivety and cluelessness in so many situations that Frasier repeatedly calls him a ninny, nit, boob, and idiot throughout the series.