The finely tailored crowd at the Shoreham Americana Hotel roared with pleasure, mayor Walter E. Washington was talking publicly in a rare down-home way about how he has responded to the controversies and crises of his administration in recent months.

Before he had risen to speak, his wife Bennetta had told the audience of more than 500 that her husband was "getting better with age." The mayor then took over, using Flip Wilson-like intonations to get his point across.

"I'm feeling good, real good." he said, shimmying slightly. "If I felt any better, I couldn't stand it. Don't ask me to prove it," he said to the muffled chuckles of many of the women present.

"I'm tired right now." He added. "But I can handle it."

"You see," said the mayor, leaning back from the podium, tilting his head to the side, "some of you jump in it all at once. You give it up all at one time. I got my style. Do it my way - and you live longer."

It was the mayor's 62d birthday, and this was his party, given by a group called "Friends of the Mayor." The event on Friday night was billed as a nonpolitical affair, a $25-a plate dinner to raise money for a Walter Washington archives to house the memorabilia of his administration over the past 10 years.

But it was clearly more than that. The event, which had as its theme "unification," seemed aimed at making a public display of support for the mayor, this head of the District's first elected city government more than 100 years.

In recent months there has been an atmosphere of crisis around city hall as newspapers reported allegations of nepotism, cronyism and leasing irregularities in the Department of Human Resources, formerly headed by Joseph P. Yeldell. Similar allegations of nepotism have been published about the city Department of Recreation, which is headed by William Rumsey.

Seven city reports from investigations of the allegations against Yeldell have turned up no hard evidence of impropriety on Yeldell's part. The mayor, who suspended Yeldell as head of DHR, has announced that Yeldell will become general assistant to the mayor with the same salart he received as head of DHR.

The U.S. Attorney's Office is still investigating allegations of conflict of interest in Yeldell's dealings with developer and millionaire parking building magnate Dominic F. Antonelli Jr.

In addition, some business and financial leaders, social activist city government employees and longtime allice of the mayor have complained, most often privately, that the new home rule government is inefficient and unresponsive.

At Friday's gathering the mayor never specificially adressed the criticisms and allegations concerning his administration. Referring to newspaper accounts, quoting "sources," Washington said, "It would appear that we were having serious problems in the last few months. But some of the allegations were false. That's what happens when you depend on reliable "sources." The crowd applauded enthusiastically.

"I think home rule is sounder than many of you think it is," the mayor said, "And it is in good hands."

Washington said he knew that some of the guests present came because they wanted to, "and some of you came because you wouldn't dare not come. It's not always easy for the City Council to come to birthday parties, especially mine." The mayor apparently was referring to disputes between his office and the Council. "That takes courage," he said.

Sounding as if he might run for the election next year, Washington said, "Those of you who have problems better watch out, because I'm feeling mighty good.I've got more friends than you might think," he said.

"The distance that this city has come since 1954 is great," Washington said. "It is so easy for some to forget that 10 years ago this was a colonial city. Now we do have a medium of home rule, but without your help and support, we won't get the things you really need and want."

Without being specific, Washington said there were "for us at Work to create and feed upon disunity in city government. They're trying to make that disunity so pervasive as to make it impossible for us to sit together, to communicateand strategize about the future."