Updated June 1, 2012
The Grand Ballroom scene is the Haunted Mansion's masterpiece, a jawdroppin', show-stoppin', eye-poppin',
Actually, dancing etiquette was the least of the problems they had with the dancers. They almost had a disaster with this effect, but that bit of trivia has lain quietly hidden. Sometimes something is "long forgotten" because someone swept it under the rug and hoped that it would be forgotten.
The effect itself is simple, just a bunch of mannequins spinning on turntables (perhaps too simple—Rolly Crump has been known to criticize it as too obvious). There are six couples in all, two sets of three on two adjacent turntables. The blueprints tell the story.
Strangely enough, in some early photography, there are only three couples, not six. That's what you see in this pre-opening publicity photo, probably taken in the summer of 1969:
It's even on film. Filming the interior of the HM has always been difficult, so the detailed ride-thru footage done by WDI (then WED) for their own in-house use quickly became available in edited form as stock interior footage for the HM. It's endlessly recycled, and you still see snippets of it any time they want to show something inside the Mansions. The famous Disneyland Showtime TV episode featuring the Osmond brothers (aired March 22, 1970) made heavy use of the WED footage. The main point of interest here is that this film was shot well before the HM opened, once again, probably during the summer of 1969. And in the ballroom scene, there are only three couples swirling around ("You can see right through the dancers!" says Donny. Yep, and it doesn't take long, since there aren't very many to see through.)