It's hard to put a finger on, but there's a strange mixture of elation and queasiness in the air as Mayor Marion Barry's administration leads the District in celebrating 10 years of home rule.

A lot of it has to do with attitudes about the mayor himself.

During his six years in office, the former street activist and City Council member has done much to vindicate early home rule proponents who insisted the District was capable of conducting its affairs independent of Congress and the White House.

Barry has largely straightened out the city's most serious financial problems, brought a sense of order and purpose to the city bureaucracy and occasionally hit on an initiative or program that made a difference to the lives of D.C. residents.

Also, few can doubt his political acumen. He has a long, unbroken series of political victories to his credit. And he raised his national profile by jumping aboard Jesse Jackson's presidential campaign and, most recently, taking a highly visible leadership role in condemning violence against abortion clinics.

But like other big city mayors, Barry for years has been dogged by troubling rumors about the way he conducts his personal life and the honesty of some of the people he has placed in positions of trust.

Last year, this problem went far beyond the rumor stage.

To wit: The executive director of the D.C. Commission on the Arts and Humanities resigned in disgrace and was convicted of stealing commission funds.

The executive director of the D.C. cable television design commission quit after it was disclosed he had been involved in a cocaine ring.

Two employes of the Department of Employment Services and a private contractor were fired after the mayor publicly confirmed they had misused city funds.

D.C. Auditor Otis Troupe criticized the Barry administration for handing out consulting contracts to a number of former city officials.

And early last month, The Washington Post reported that former deputy mayor Ivanhoe Donaldson, Barry's most trusted political adviser, was under investigation by a federal grand jury for possible misuse of city funds while he headed the D.C. Department of Employment Services.

That report sent shock waves through the administration and the city's political establishment. It also took a little of the zing out of last week's celebration of home rule.

Barry, too, was linked to a grand jury investigation -- the one into drug use by city employes that resulted in the conviction of Karen Johnson, a former mid-level employe of the D.C. Energy Office. The mayor was called before the grand jury last January to testify in the case, after a government informant got Johnson to tell him that she had sold cocaine to the mayor on numerous occasions.

But Johnson refused to testify before the grand jury and federal prosecutors lacked evidence to prove that Barry had done anything wrong.

Barry's lawyer acknowledged that the mayor had had a "personal" relationship with Johnson, but denied that Barry had ever purchased drugs.

With that as a backdrop, Barry begins his seventh year as mayor, with much accomplished, much left to be done and his political future a bit murky.

The mayor contends that hispersonal and political popularity is "at an all-time high" and that he would have no problem winning election to a third term in 1986 -- which now appears to be his plan.

A recent survey of D.C. residents by The Washington Post seems to bear out his contention, to some extent.

When asked to rate the job Barry is doing as mayor, 65 percent of the respondents said he was doing a good or excellent job.

But Barry's approval rating dropped markedly when the 836 adults interviewed Dec. 9 to 14 were asked about Barry's performance in making sure that top Disrict officials have high ethical standards.

On that issue of ethics in government, 51 percent approved of the mayor's performance, while 32 percent indicated they disapproved.

Barry said he has some detractors who are willing to say or believe just about anything about him.

But he contends that the majority of people believe he is personally honest and has "great integrity."

"They believe I tell the truth," he said last week. "And they believe I don't tolerate corruption in government."

Few can dispute that Barry has matured a lot in six years and has developed a keen political antenna for what it takes to enhance his own image and that of the District.

Late last year, he and other city officials scored important victories on Capitol Hill and Wall Street. And already there is talk that the Republicans -- pleased with the treatment they are getting from the city in preparing for President Reagan's second inauguration -- may hold their 1988 national convention here.

The city has much to look forward to and Barry is well positioned to take credit for much of the glory. It would be tragic if all of that were undercut or diminished by the lingering doubts about the ethical standards of his administration.