Joan Mondale, the Carter Administration's designated advocate of the visual arts, yesterday made a state visit to the capital of the art world.

She flew here on the shuttle, walked among the warehouses that lined the streets of SoHo, visited half a dozen of the better downtown galleries, lunched with representatives of New York's art establishment, went afterward for an hour-long visit to the Harlem School for the Arts and later gave a brief, encouraging address to those patrons from the world or commerce on the Business Committee of the Arts. She also planned to visit P.S. 1, an 1887 public school that is now a center for experimental art, before returning to Washington today.

Nothing much happened, but the mood throughout was mellow. Mrs. Mondale, who calls herself "the government's lightning rod for art,"

"I can't learn just by sitting in Washington and reading magazines," she said. "I have to see things for myself."

She was works by Robert Rauschenberg (and Rauschenberg himself), Roy Lichtenstein's minimal sculptures (and Lichenstein himself) astract paintings, photorealist canvases, and an elegant residential loft, which was once a chocolate factory and is now where dealer Louis K. Meisel lives above his shop.

The frist gallery she visited Sperone, Westwater, Fisher, on Greene Street, was showing the floor sculptures of Carl Andre. Surrounded by an entourage of photographers, reporters, and television technicians, she smiled, without bafflement, at Andre's rectangles of metal, steel, copper, zinc, arranged on the floor.

"Now what the hell are those things?" asked a Secret Service man, who then caught himself immediately "I'm afraid I have no understanding, no art appreciation" he apologetically explain.

There was a time when politicians and members of their entourage, would have sneered at modern abstract art. Mrs. Mondale, however, promotes it. "Her visit won't change the world, but it surely will not hurt," said dealer Angela Westwater. "Who else has come around?"

Mrs. Mondale is a veteran compaigner. She spent more time shaking hands with gallery clerks than she did with their bosses. Shen she found herself surrounded by art world stars, as she did at lunch, she talked straight through the meal.

At Ballato's, a small Italian restaurant on East Houston Street, which critic John Canady calls "the place where artist eat," she dined with painters Jasper Johns, Lichentenstein, Rauschenberg, and Washington's Ed McGowin and Claudia De Monte, with sculptor Louise Nevelson, with dealer Leo Castelli (the host) and critics Robert Hughes of Time, Thomas Hess of New York magazine and Calvin Tomkins of the New Yorker.

During the lunch, she confided that her favorite statistic was the cost of public relations for the Defense Department which was "greater than all the money spent on the arts" by the government. "I mean, that is so incredible," she added.

She said, "You are the establishment. You have already been rewarded. I would like to help living American artists less fortunate than you. What should I, what should our government do?"

William Walton, an old friend, a sophisticated politican, a former chairman of the national Commission of Fine Arts, and the unofficial art adviser to President and Mrs. Kennedy, watched Mrs. Mondale at work.

"Think about the past," he said. "Jackie made the White House a national museum, Lady Bird transformed the District into a spring garden. Fine. But the only wife who really mattered was Eleanor. She changed things. She attacked the system. She goaded the establishment. She infuriated many. She sometimes infuriated her husband, but she made a difference. She caused change."

"I hope one or two of you will give me some suggestions," said mrs. Mondale. "What should we do?"

"Look for the authentic," said Jasper Johns. "Encourage creativity," said Nevelson. "We believed there was no one in Washington turn to. It's heartening to know you are the first," and Hughes, "Roy must say three words," said Leo Castelli, his dealer. "Thank you for coming," said Roy Lichtenstein.

Rauschenberg, who runs Change, Inc., a rescue organization for needy artists said, "You can't give money to everyone who asks. We have a form letter. It says 'o out and get a job."