All eight members of the Fairfax County Board of Supervisors present at a Monday meeting voted in favor of requiring county agencies to report how much they spend on legal fees. It was incorrectly reported yesterday that Supervisor Audrey Moore of Annandale dissented.

The first week the new Metropolitan Boys' and Girls' Club at 14th and Chapin streets NW was open, the gymnasium floor, made of a rubber compound, became so slippery from the humidity that the gym had to be closed.

The club, opened with fanfare by city officials less than two months ago, has no air conditioning, windows that don't open, one broken floor fan and a mechanical ventilation system that circulates hot air.

The lack of some sort of cooling system at the club to combat Washington's steam-bath summer weather has sparked a neighborhood squabble. Several community activists are pushing for installation of an air conditioner, while spokesmen for the Boys' Clubs of Greater Washington say the organization can't afford one. In any event, they add, many of those who use the club--from neighborhood youngsters to those in their early 20s--haven't been complaining.

On a recent day, for instance, when the temperature had reached 91 degrees, some club users said they felt the heat, but many said it was not bad enough to keep them away. "It's the best you can do unless you go to a university," said Bert Gaye, 21.

David King, 21, said, "It's hot in here, but that's natural in a gym. . . . To be honest with you, it is a nice gym."

Dr. Bette L. Catoe, a pediatrician in private practice who gave physical examinations to some of the children at the club going to summer camp in early June, said she came away concerned about the lack of air conditioning.

"From a physician's standpoint I was concerned because this is an unhealthy situation," Catoe said, citing heat exhaustion, respiratory problems and muscle cramps as possible hazards.

"And I was even more disturbed when I found the board knew there was no air conditioning and this was an economic measure," she said. "I realize it's hard times, but some grants or public monies could have been solicited."

Ibrahim Mumin, executive director of the Shaw Project Area Committee, said, "Frankly, I was shocked that a brand-new building for $1.3 million was built without air conditioning." Mumin, along with several others, voiced concern that the building presents a potential health hazard to youngsters.

"The kids don't complain," said Rafael L. Alaniz, the club's coordinator. "All they want is to play basketball. . .The main thing is that the building is here and the kids are in it."

Jerry Steele, director of the Boys' Clubs of Greater Washington, said, "I know those people on 14th Street are complaining, but we're out there busting our humps trying to raise money for the place and that area didn't give us one nickel."

"The kids don't complain," said Rafael L. Alaniz, the club's coordinator. "All they want is to play basketball . . . The main thing is that the building is here and the kids are in it."

The modern, blue-and-white facility was opened after eight years of planning on May 25, with Mayor Marion Barry and other city officials in attendance. It sits in an area notorious as an open-air illegal drug market, a neighborhood whose recovery from the 1968 riots has been painstakingly slow.

The center has a multipurpose gym, men's and women's locker rooms with hot and cold showers, a kitchen, two small offices, and recreation rooms that include space for a future library. It offers sewing classes and special events such as movies, roller-skating and dances.

The facility was designed with air conditioning, said its architect, Paul Clarke, but the Boys' Clubs ran out of money. Its windows don't open, Clarke said, to increase security and to help insulate the energy-efficient building.

Steele says the Boys' Clubs can't afford to add the air conditioning. The organization still owes $50,000 on the building, he said.

Monroe Stewart, chief of the engineering branch of the city's Building and Zoning Administration, says D.C. law does not require operable windows or air conditioning, only mechanical lighting and some kind of ventilation. The noncooling ventilation system now in place satisfies the requirements.

"It's a human violation," Mumin said. The citizens advisory council did not ask about air conditioning when it met with Boys' Club officials two months before the club opened, he said, because in 1982 "that's like asking about toilets to me."

Edna Frazier-Cromwell, head of the advisory council, said her group is currently negotiating with the building's contractors and the Boys' Clubs for installation of an air conditioner, and would be willing to contribute some, but not all, of the cost.