At the Kennedy Center it was a salute to Howard Mitchell, for 20 years the music director of the National Symphony Orchestra and back in town this week as part of the NSO's 50th anniversary year. A few blocks away at Lisner Auditorium yet another salute was going on, this one to Mstislav Rostropovich, the symphony's current music director celebrating the 25th anniversary of his first performance here.

That was Washington last night, an embarrassment of musical riches for a town once considered a cultural backwater. And the coincidence of dates seemed even more striking as the State Department disclosed it was working to grant asylum to Soviet conductor Maxim Shostakovich.

"We'll get them all over here pretty soon," said Mitchell, when told of the negotiations during a post-concert party at the National Academy of Sciences.

Secretary of Defense Caspar Weinberger, who knew about the possibility, had not commented on what Shostakovich's defection symbolized back in Russia. But he called it "very nice to have a great musician like him coming to the United States. And I'll look forward to hearing him."

William Middendorf, ambassador-designate to the Organization of American States, said it was "another example of the decadent system in Russia if they can't keep a great conductor like Shostakovich from leaving. It'll be a tremendous lift to the music world here."

Deputy Secretary of State William Clark, who with Secretary of State Alexander M. Haig Jr. attended the Mitchell performance, said there was a message in the defection. "Not ours. Theirs."

Only officials had known that Shostakovich was trying to come to the United States. For the rest of the 130 at the post-concert supper, it was primarily Howard Mitchell's evening.

"It's glorious to be back. I'm so grateful, always so grateful for what this country means," Mitchell told the black-tie crowd dining on roast lamb and rice with appropriate wines.

As it happened, few of the people who run the National Symphony could make Mitchell's party because of the Rostropovich fete at the Lisner.

"We didn't invite them because we didn't want to have any kind of competition in the symphony family," said Lillie Lou Rietzke, the evening's chairman. The performance had been postponed from its original December date when Mitchell had become ill.

But there were some high-powered Reagan Cabinet officers on hand as well as plenty of old friends of the former maestro from those other years when Mitchell was the crown prince of culture in Washington. some, like Ethel Garrett, even flew in by private jet just to be on hand for the festivities.

"I wasn't planning to come back until after Easter, but Lillie Lou was desperate about this thing because there aren't many of us Mitchell girls left," said Garrett, one of Washington's reigning grande dames.

It was she, according to Rietzke, who came up with the added reason to celebrate: the recovery of President Reagan from his gunshot wound.

"Ethel said we should call it 'a celebration of gratefulness and thankfulness,'" said Rietzke.

There were a number of ambassadors in the group, many representing countries in Europe and South America where the National Symphony has gone on tour. And joining everybody at the party was the symphony's guest soloist, violinist Eugene Fodor, who drew rave reviews from the crowd.

After his performance Fodor slipped into a box seat and read the program notes while Mitchell conducted Hindemith's "Mathis der Maler." During the loud parts he talked to his wife.

Mitchell received tributes from the Washington Metropolitan Police Boys and Girls Clubs for his efforts to familiarize young audiences with symphony music. And Nancy Thurmond, whose husband Strom is president pro tem of the U.S. Senate, offered still another salute. For his "candor, courage, charisma, character and compassion" in bringing music to all ages, he has become " a national treasure," she said.