L.A. knows how to put on a variety show. But few productions brought together such an assortment of players and characters from across the city than a surreal talent show broadcast nationwide in 1987.

The Parkettes gymnastic organization raised more than $78,500 at Saturday’s nine-hour telethon, far exceeding its goal of $60,000 and the $51,000 raised last year. “We were extremely elated,” said ...