The D.C. Board of Education and the Washington Teachers' Union nominated a former city Labor Relations Board chairman yesterday to head a special fact-finding panel that will attempt to settle disputes that led to last month's 23-day teachers' strike.

James M. Harkless, a private arbitrator who served as a fact-finder in a 1975 contract dispute between the school board and the union, was proposed as chairman of the new three-member panel, according to board and union officials. Harkless said last night that he had not decided whether he will accept the job.

Under a court order, the fact-finding panel must make recommendations by June 15 on a series of contract disagreements between the union and the school board. The panel also will include a union representative, Marvin Friedman, and a school board representative, Stephanie S. Cabinss.

Meanwhile, the Board of Education failed to decide, after a closed-door session early yesterday evening, whether it intends to appeal the order by Superior Court Judge Gladys Kessler that prompted the union to call off its strike last week.

Some school board members have criticized the order because it is designed to reinstate the union's former contract until July 15. Board negotiators have objected to many provisions of the old contract. The board's refusal to extend the former contract for a fourth time in February led to the teachers' walkout.

After yesterday's board meeting, board President Minnie S. Woodson declined to say whether the court order will be appealed. "Things are status quo," she said.

One board member, R. Calvin Lockridge, contended that despite the court order, the contract is not currently in effect because the board has not formally reinstated it. Lockridge said he will oppose board action to reinstate the contract.

William B. Peer, a lawyer representing the union, later disputed Lockridge's view. "The court reinstated the contract," he said. "The [court] order is self-executing."

Yesterday school officials reported that about 80 percent of the city's 113,000 public school students attended school-slightly below the school system's normal attendance rate of 87 percent. About half the city's students had stayed away from school during the strike. The attendance rate had risen to 63 percent on Friday, according to school officials.

Attendance among the city's more than 6,000 public school teachers was described by school officials as normal yesterday, with 94 percent reported at work.

Yesterday also marked the first loss of take-home pay for teachers who took part in the strike. Pay checks were distributed at the city's 190 schools yesterday for the period of March 1 through March 15. Because the strike started March 6, the school system's total monthly payroll dropped to about $4 million yesterday, compared with about $7 million for the previous semimonthly pay period, according to school officials.

At Lincoln Junior High School on 16th Street NW, as at schools throughout the city, teachers who had joined in the walkout picked up sharply reduced pay checks yesterday afternoon. Some said they plan to take summer jobs, cut into their savings, postpone paying their bills or go to fewer restaurants and movies to make up for their losses in pay.

"The economic impact is tremendous, but psychologically I think I did the right thing," said Lawrence Berry, a mathematics teacher at Lincoln, whose paycheck yesterday amounted to only $89.50. Normally, he said, his semi monthly take-home pay is about $425.Berry said he plans to work during the summer as a house painter and tutor to help recover his financial losses.

Beverley Crockett, an English teacher at Lincoln, received about $300 less in yesterday's paycheck than her normal take-home pay. But she said, "If I had to do it again I would-if it had taken longer, I would still be out (on strike)." Crockett said her family plans to postpone paying several bills and to take out a loan of more than $1,000 to bridge their financial gap.

Teachers who stayed off their jobs for the entire strike will receive even smaller paychecks for the next pay period, which covers March 16 through March 30. The strike ended March 29.

A Superior Court hearing has not yet been scheduled to determine what amount the Washington Techers' Union may be fined for striking in defiance of a court order. Under the school board's interpretation of a previous court order, the union and its leaders could be fined more than $1 million. The union contends any fines should be considerably less.