Top jobs at the Health and Human Services Department, left open by resignations and shifts, are going unfilled. The most important is that of the Social Security commissioner, head of the $180 billion-a-year Social Security old-age and disability program, the single largest in the government. The commissioner also administers cash welfare programs such as Aid to Families with Dependent Children (AFDC) and the Supplemental Security Income program.

When John A. (Jack) Svahn became undersecretary of HHS nearly three months ago, he technically gave up his job as commissioner. Since no one has been named to replace him, he is said to be keeping an eye on the store.

Also unfilled is the job of assistant secretary for public affairs, left vacant when Pamela Bailey went to the White House. Claire del Real, formerly Bailey's deputy, is holding down the post on an "acting" basis. Insiders say interviews are being conducted to pick successors by the end of the month.

Nor has the job of director of the Office of Family Assistance, formerly held by Linda McMahon, been filled permanently. McMahon left to work for former undersecretary David Swoap, who now heads California's health and welfare system. JoAnne Ross, a former McMahon deputy, holds the top spot of the office that runs the AFDC program on an "acting" basis. * * *

FEUD AT THE TOP? . . . Insiders say Secretary Margaret M. Heckler and Svahn have not developed the kind of "close, warm working relationship" many had hoped they would in the three months since they took their current jobs.

The problem was caused in part, it is said, by media speculation that the department would really be run by Svahn, who has close ties to the White House after his service as a top welfare official in the California state government when Ronald Reagan was governor.

Heckler, a take-charge kind of person, wouldn't accept that idea, however. "But the relationship is better today than a week or a few weeks ago, and it has been slowly but steadily getting better," one source said. * * *

SOCIAL WORK BOOM . . . The growth of federal social programs has helped stimulate growth in the number of jobs in social work, partly because of federal funding, but mainly because of new attitudes about the need for services that are then financed by local governments and private agencies, according to officials at the National Association of Social Workers.

The NASW, in an analysis of figures compiled by the Census Bureau, says that the number of social workers in the United States has jumped from 218,000 in 1972 to 461,000 in 1980. About half are professionally trained social workers with college degrees in the field and the others perform various jobs that do not require a degree.

Jobs that are funded in part by the federal government include those in social service departments of hospitals, where social workers provide Medicare patients and their families with information about such things as transportation, nursing homes and home health care services. Medicare reimburses the hospital for part of the costs of social service departments.

Under a proposed HHS regulation that would change many hospital rules, hospital social service departments would no longer have to be headed by social workers with master's degrees or the equivalent. HHS proposed the rule in January, and it is pending. * * *

WASTE UPDATE . . . The HHS inspector general's semiannual report, released this week, outlined proposals it has made over the past six months that it said could save as much as $669 million in the next year. They included improved procurement of pacemakers, changes in certain welfare administration practices, elimination of what it called unnecessary recertification of nursing homes, improved efforts to get money back from some grantees and contractors, and improved procurement of laboratory services. * * *

EASING THE PURGE . . . HHS officials are putting the final touches on proposals to ease conditions for people threatened with removal from the Social Security disability rolls. Since 1981, the Social Security Administration has reviewed 768,000 beneficiaries and has ordered 355,000 off the rolls, although 88,500 have been reinstated on appeal.

Public protests against the department's alleged excessive zeal and superficial review procedures have become its biggest political headache. Both the House Ways and Means and Senate Finance committees are planning major inquiries into the review process.