The Carter administration is preparing to make its first major nominations for District of Columbia jobs - four long-vacant D.C. Superior Court judgeships - amid growing concern among some lawyers about a worsening backlog of cases caused by a shortage of judges there.

The nominations for local judgeships are one of the few remaining areas in which the President can make a significant direct impact on District affairs. The handling of the appointments by President Carter and his staff is seen as an indication of the administration's concern with the quality of the local bench here.

Members of the White House staff said they actively are reviewing the names of 12 judicial candidates submitted last fall to the Ford administration by the local judicial nominating commission. The White House staff hopes to make its four selections from among the 12 names in the next couple of weeks. The Senate could then vote on the names.

The filling of the four existing vacancies may not be the only way in which Carter will have a quick impact on the 44-member local bench.In addition to the four already announced vacancies, a fifth judge is seriously ill, a sixth will retire later this month because of age, and considerable controversy and litigation surrounds the right of a seventh judge to continue to sit.

Also, a successor must be found for D.C. Appeals Court judge Austin L. Fickling who died last weekend. Appellate court appointments also are handled by the local nominating commission, which narrows down the field of selection before sending its suggestions to the White House for final approval.

D.C. Superior Court Chief Judge Harold H. Greene discounted any suggestion that a major crisis was developing at the trial court level, but conceded that "any reduction in judicial personnel is bound to be a problem."

"We are generally short and now we are a little shorter," Greene added. He said he had expected the months-long delay because of the change in administration and the Congressional recess, and "I'm not being critical of anybody. There's nobody to criticize."

Both prosecutors and defense lawyers as well as civil attorneys who practice in the court regularly, say privately that it seems to be taking longer to schedule trials there. One prosecutor noted there are fewer judges to handle felony cases, and said he feared that a serious backlog could develop if the new judges are not named soon.

"I don't care who is chosen to fill the vacancies, as long as they are qualified," said the prosecutor, who refused to be quoted by name. "I just want enough judges available to hear cases quickly."

Associate White House Counsel Dough Huron, who is one of the three main people in the Carter administration working on the judicial vacancies at this point, said he has examined the statutes dealing with judicial appointments here and has discussed it with others in the administration.

"This is a matter that is being given high priority," Huron said in a telephone interview. He said that the initial screening for the jobs will be done by him, White House-D.C. liaison Martha Mitchell and Jim Dyke, a special assistant on the staff of Vice President Walter Mondale.

Ultimately, other top level White House advisers and the President himself will become involved in the decision, Huron added.

Huron said that staff members working on the vacancies will be contacting various bar groups and individuals familiar with the court system here to select the best persons for the slots.

Last December, the D.C. judicial nominating commission sent nine names to the White House from which it could choose three to fill that number of Superior Court vacancies. A similar process had been followed earlier in the fall, when three names were sent to the White House for an earlier Superior Court vacancy.

President Ford moved to fill those vacancies by submitting to the Senate the names of Robert M. Scott, and attorney in private practice; Annice McBryde Wagner, the people's counsel for the D.C. Public Service Commission; Robert A. Shuker Jr., chief of the U.S. Attorney's office Superior Court division, and Edwin C. Brown Jr., a former Justice Department lawyer who is now in private practice here.

The Senate did not act on those names, and President Carter withdrew them from nomination two week ago. There is some legal question as to the procedure to be followed now, since the statute conerning judicial appointments here gives the White House only 60 days within which to act on the nominating commission's suggestions.

However, Huron said the White House has determined in examing the statute that it can select any four names from among the 12 that were submitted to the White House last fall. The White House also has concluded that the days referred to in the statute concerns days in which Congress is in session, not calendar days, and thus there is still time to act on the commission's nominations.

The White House could resubmit the same four names, choose four totally different names from among the 12, for choose a combination of those.

The four Vacancies being filled are those of Judge George W. Draper II, who died last fall; Judge Theodore R. Newman Jr., who was named the chief judge of the D.C. Court of Appeals; Judge Harry T. Alexander, whose term expired and who did not seek re-appointment, and Judge Richard R. Atkinson, who retired because he is over 70 and not eligible for reappointment.

Judge James A. Washington, who fell down a flight of stairs in his home, is seriously ill, and his future on the bench is uncertain. Another Judge, Milton D. Korman, reaches retirement age later this month and is not eligible for reappointment.

Judge Charles W. Halleck continues to be in legal limbo after more than a year of controversy surrounding his reappointment.

He was found "qualified" for reappointment by the D.C. judicial tenure commission in the fall of 1975, and his name was sent to the Senate by President Ford. The Senate never voted on his appointment, apparently because of continued controversy about statements he made on and off the bench.

The tenure commission then began formal disciplinary proceedings against Halleck, who in turn filed suit challenging the commission's procedures and authority. He lost the first round of that suit in U.S. court but is appealing the decision.

The White House can resubmit Halleck's name at any time despite the suit, and disciplinary proceedings, however, and attempt to bring it to a vote in the Senate.

Huron said the White House is aware of the Halleck situation, and "we have to make a decision. It's also being given priority."

Huron added, though, that the timing of the Halleck decision is not as urgent as for a decision to fill the four existing vacancies. This is because Halleck is still a sitting judge and carrying a normal load of court work, he said.

The commissions of two other judges - Alfred Burka and John D. Fauntleroy - will expire this June. There is no indication as to whether either man will seek reappointment at that time.

Although the selection process as outlined by White House officials may ultimately involve the President himself, it appeared that a major part of the work would be done by Mitchell Huron and Kyke. According to present White House plans, the three will be playing important roles in all of the administration's relations with the District.

Mitchell, 36, has been in Washington since 1968, when she became assistant director for student activities at Federal City College. Prior to that time, she had worled in industrial relations for U.S. Steel in Gary, Ind., and taught high school there. After four years at FCC, she became deputy director of the National Institute for Drug Programs here and then was named director of the information division of the Drug Abuse Council, Inc.

Huron, 31, comes from Highland Park, Mich, got his law degree from the University of Chicago in 1970, and joined the Justice Department's civil rights division the same year. He specialised in employment discrimination cases at Justice. He resigned last April to work in Mr. Carter's campaign organization. His White House job description says he "will be responsible for organizing the paper flow to and from the President."

Dyke, 30, is a special assistant to Vice President Mondale for issues and development. He got his bachelor of arts and law degrees from Howard University here and worked for the prestigious law firm of Covington and Burling. He was counsel to the Democratic platform committee and then jointed Mondale's campaign staff as a political adviser. His present duties include working closely with Mitchell and serving as Mondale's personal and political liaison person with the District government and the city's black community.