Republicans always enjoy complaining about "the mess in Washington," but these days the "mess" they are most upset about is the Reagan administration's appointments process. It's under attack from many quarters for inefficiency, delay and ideological in-fighting.

Across the senior ranks of government, many important sub-Cabinet positions remain unfilled. In some awkward cases, people are working in jobs for which they are still not officially nominated. And, in a few cases, people started at work in high-level posts, only to discover that their appointments were vetoed for political reasons. Most of the criticism is being aimed at the White House itself, particularly the personnel office and the political liaison operation run by Lyn Nofziger.

Officially, all is well at the embattled personnel office presided over by E. Pendleton James, a California executive headhunter who was originally tapped for White House recruitment by presidential counselor Edwin Meese III.

Meese and White House chief of staff James A. Baker III have statistics to show that President Reagan is making his major appointments faster than Presidents Carter and Kennedy did -- though not as quickly as President Nixon and Eisenhower.

But these statistics are little comfort in the several departments where major jobs are unfilled and bitter feuding continues over prospective appointments. The result, according to the critics, is that important policy decisions are being sidetracked or delayed.

At the Department of Education, the Cabinet secretary's handpicked undersecretary was rejected by the White House -- three weeks after he had been designated for the job.

At the Pentagon, five of seven assistant secretary of defense slots remain unfilled along with virtually all of the civilian assistant secretary jobs in each of the military services.

At the Department of Energy, none of the eight assistant secretaries has been chosen. One unhappy official remarks: "The interesting thing is the paucity of rumors."

Back at White House personnel, the harried and oft-criticized James says that "the facts don't support the accusations." He particularly disagrees with an impassioned criticism delivered by John Lofton in the February issue of Conservative Digest which complains that James' personnel office is passing over Reagan loyalists in favor of "retreads from the Nixon and Ford administrations." The magazine urges that James be fired.

James -- backed by Meese and Baker -- says that "adherence to the philosophy, policies and objectives" of President Reagan has been the first criterion of the appointments process.

In some of the Cabinet departments there is agreement with this official view, but not necessarily much sympathy for it. Some administration officials tell tales of what one of them calls "an obsession" for Reagan loyalism. They say that competent and conservative Republicans have been rejected for some positions for which they are qualified because of vetoes exercised by political adviser Nofziger or because of fear in the personnel office of "New Right" criticism.

And others who are relatively unconcerned about the ideological aspects of the appointments process say that the James office is so bogged down in paperwork it isn't getting even the uncontroversial appointments put through in time.

There is criticism from the personnel office about the departments, too. One personnel insider recently drew up a report card on how the departments organized in the early weeks of the Reagan administration. He gave 'A's" to only four departments -- State, Transportation, Interior and Treasury. His lowest grade, a politely high one of "C," went to Education and Energy.

But the view at the Department of Education is that the main problem is the White House clearance system.

Consider the case of Christopher T. Cross, a former minority staff director on the House Education and Labor Committee, who was selected by Terrel (Ted) Bell, the secretary of education, as his undersecretary. Three weeks after Bell made the choice, Cross learned that his appointment had been killed by the White House, although he was never told why. As far as anyone knew, his Republican credentials were impeccable, and he had helped Office of Management and Budget Director David A. Stockman design education budget strategy during the transition.

The word from within the White House is that Cross was opposed by the conservative Heritage Foundation, as influential force in the transition selection process, and by other unnamed conservatives, on grounds that he had not been involved in any of the Reagan campaigns.

The rejection took three weeks and forced Bell to start again through the complicated appointments process. As of yet, he has no undersecretary. Ironically, his new designated choice for the job is another House staff member -- William Clohan, who was hired for his job by Cross.

Since Clohan had been Bell's choice for department counsel, this left another vacancy, which is now scheduled to be filled by Dan Oliver, a conservative who is described as unfamiliar with national education policy.

James, confirming the rejection of Cross, says it shows that "the system is working." The system of which he speaks has so many built-in checkpoints that the wonder of it, as one survivor of the clearances puts it, is "not that it works slowly, but that it works at all."

The first step in the process is for the department secretary to submit a name of a prospective appointee to the personnel office. James then submits it for a politcal check, which is Nofziger's responsibility, and a policy check, by Richard V. Allen if the appointment is in the State or Defense departments and Martin Anderson if it is a domestic department.

But that's just the beginning. The nominee then must go through the FBI checks and other checks for ethics and conflicts of interest, plus a local political check by the personnel office.

After all this, there's still a final check with hometown congressmen to see if they have any objection.

If the nominee is still in the running, his name is taken up in a daily 5 p.m. meeting attended by James, Meese, Baker and his influential deputy, Michael K. Deaver. The names are then submitted to the president by James, who usually meets with Reagan twice a week.

This formal procedure can be set aside with interventions from other White House officials, members of Congress and members of Reagan's wealthy "kitchen cabinet." The "kitchen cabinet" members are heroes to many conservatives because it it believed that they raised the banner of Reagan loyalism on several disputed appointments.

While there are many different points of view even within the White House inner circle about how well the appointments process is working, there is general aggreement on some key points:

The Reagan administration is paying now for slowness of some of its Cabinet appointments, which forced delays all along the line with lesser jobs. This in turn generated grumbling and political pressure from Reagan campaign workers who were destined for these lower-level jobs. The Reagan policy of "firing all the political nominees," as Baker puts it, left large gaps in many departments even though the appointments process was ahead of the Carter pace. As both Baker and Meese describe it, this was a calculated decision made on the grounds that it was better to work shorthanded than to have holdovers who might be at cross-purposes with Reagan policies.

Even the staunchest defenders of James say that there was a slowing down in the appointments process when his principal deputy, James Cavanaugh, decided to return two weeks ago to the pharmaceutical company he heads in California.

Those Cabinet secretaries who are either close to Reagan, like Secretary of Defense Casper W. Weinberger, or who have independent stature, like Secretary of State Alexander M. Haig Jr., were able to select their own deputies even against formidable opposition.

But lesser secretaries wound up, as Bell did, with their choices overruled for political reasons. Besides Weinberger and Haig, three other Cabinet members have enjoyed notable success -- Attorney General William French Smith, who is a longtime friend of Reagan's and a member of the "kitchen cabinet," Secretary of the Treasury Donald T. Regan, because he organized quickly, and Secretary of Transportation Drew Lewis, a trusted compaign operative. Nonetheless, there are still significant vacancies in all of these departments too.

Nofziger, because of his role in appointments, has established important standing as an effective conservative in-fighter. His advocacies, however, have not been limited to the so-called "movement conservatives" who engage in organizational activity but have embraced a variety of persons whose activity over the years has been largely limited to Reagan campaigns.

We have to remember the people who brought us here," a White House aide quotes Nofziger as saying frequently. Among campaign workers, Nofziger has earned the reputation of being their most trusted friend in the White House.

Campaign connections do count, if they are good connections. For instance, without fanfare, Reagan political advisor Stu Spencer won the appointment of his choice -- a man who is also the choice of doctors whom Spencer represents as a consultant in California -- for a key post in the Department of Health and Human Services. Nofziger proposed and won the appointment of a friend who had been an important fund-raiser for Reagan as the White House recruiter of women in government. Former campaign aides close to Meese or other key Reagan operatives are scattered around the labyrinth of the federal government.

James contends it is impossible to satisfy very many people in a process where there are 10 to 15 rejections for every appointment that is made. Even so, the volume of the complaints has been a bit of a surprise to James, who said last week, in reponse to the complaint that he has been insufficiently ideological: "For years I thought I was a conservative, and now I find I'm not even considered a Republican."