When the search committee trying to pick a new District of Columbia school superintendent narrows the field of 10 candidates to six finalists in the next two weeks, it will be faced with three major problems:

Four of the 10 come from school systems that are much smaller in size than the District's; only four of the candidates have any inside knowledge of D.C. schools and several of the top contenders are white.The school board began the search two months ago with the announced intention of trying to find a black educator with experience in a large urban school system, if not the D.C. system.

"I am less than thrilled" with the 10 semifinalists, board member R. Calvin Lockridge said angrily yesterday. "[Those people] from those little school districts should have never gotten in there."

The list of 10 includes Charles H. Durant III, a former superintendent of the New Brunswick, N.J., schools and now a Hartsdale, N.Y., educational consultant; Robert L. LaFrankie, superintendent in Bethlehem, Pa.; Donald D. Warner, superintendent in Tinton Falls, N.J., and William J. Leary, current superintendent in Rockville Centre, N.Y., and a former Boston superintendent.

Also among the 10 are Roger J. Lulow, an assistant superintendent for the Ohio state Department of Education; Luther W. Seabrook, associate director of social services in the South Bronx in New York City, and Jerome B. Jones, the Providence, R.I., superintendent and a former D.C. teacher.

The only candidates from the Washington area are Floretta D. McKenzie, former acting D.C. superintendent and a former U.S. Department of Education official; Reuben G. Pierce, the current associate superintendent for educatinal services in the D.C. system, and Andrew E. Jenkins III, the District's current associate superintendent for educational programs.

"As far as I'm concerned, to look at anybody other than the people from the metropolitan area, Jenkins, Pierce and McKenzie -- and Jerome Jones -- would be a waste of effort, school system time and money," Lockridge said.

Lockridge added that he personally felt that McKenzie, who also has served as a deputy superintendent in Montgomery County, is at this time the best choice. Although she served as acting superintendent in D.C. before Barbara Sizemore was selected superintendent in 1973, she had not previously applied for the top post.

A search committee member who declined to be identified said there are "clearly three leading candidates at this point -- McKenzie, Pierce and Jenkins."

But other members of the search committee said yesterday it was too early to declare anyone a front-runner until the personal interviews with the candidates are completed.

A second committee member, who also declined to be named, suggested that the committee might start the search process over again if it does not find a suitable superintendent among the 10 finalists.

Such a move would bolster the chances of Acting Superintendent James T. Guines, a man who badly wants to keep the job, but cannot formally apply for the job under an agreement he made with the board. He can however, be drafted by the board if they do not choose one of the 10.

The board last week picked the 10 semifinalists from an original field of 76 candidates. The semifinalists were selected on the basis of their administrative experience, educational philosophy, educational background and work experience in large urban systems.