When Mayor Walter E. Washington assembled his cabinet last February for a get-acquainted session with Martha (Bunny) Mitchell, White House Liaison with the District few expected a roll-up-your-sleeves-and-get-down-to-business session. And it was not.

The expectations were different, however, each of the last three times the city's top department heads have gathered in the mayor's conference room. Each time, the same static, superficial, almost staged atmosphere has prevailed, punctuated by odd moments of total silence and occasional levity touching on the comic.

"Mr. Mayor," City Administrator Julian Dugas volunteered during a lull in one of last week's meetings, "the police department would be proud to tell you there were no (fatal) accidents in the District of Columbia on Memorial Day. (Transportation Director) Doug (Schneider) might want to take credit for that."

"I didn't even know that," a surprised Schneider said.

At another point, the mayor - suntanned and just back from a long weekend in Hilton Head, S.C. - was exhorting Recreation Director William Rumsey on the need to be prepared for the closing of schools and beginning of summer vacation for city children. "Will the pools be ready this year?" the mayor asked.

"We opened 18 of them this weekend," Rumsey replied.

"What's the point?" one cabinet member asked privately after one of the sessions had ended. "What is the point?"

One of the most frequent criticisms of the mayor's administration has been the apparent lack of leadership shown in the day-to-day administration of the city. Different department heads often don't seem to know what their counterparts are doing critics contend, and the mayor sometimes doesn't seem to know what any of them are doing.

The renewed cabinet meetings - which have not taken place regularly since last fall - were supposed to help improve that image. Instead, they have underscored some of the continuing problems of the mayor's administration.

Cabinet members stroll in as much as 30 minutes late, many don't bother to take notes and at one point the mayor opened the floor for comments and about 10 seconds of ominous silence followed.

Last week, two cabinet meetings were necessary because Budget Director Comer Coppie was not prepared for the scheduled one, designed to be a briefing on the 1979 budget.

On another occasion, Advisory Neighborhood Commission members from throughout the city had been invited to meet with the mayor and his cabinet. The ANC representatives arrived to be told that the mayor was sick and wouldn't be coming, so they walked out.

It was late Tuesday night. The City Council was debating a resolution declaring Gay Pride Week. Council member Jerry Moore wanted to amend the resolution so Gay Pride Week wouldn't begin in Children's Day. That, Moore declared, could lead to problems.

Marion Barry became upset. For once, Barry asserted, the Council "should do what is right and not what is political.

That upset Moore. He said he resented implications that his opposition to the date of the declaration was polically motivated. "I'm not running for anything. I'm already elected," Moore said. "The person who made the remark may be running for something, but not me." arry, who is running for mayor, had no comeback.