The game of musical chairs at Foggy Bottom and U.S. embassies at the start of President Reagan's second term is proceeding without serious problems, according to State Department sources, in spite of a controversy over conservatives' charges that a "purge" is under way.

Shortly after Congress returns next month, the White House is expected to nominate about a half-dozen senior departmental officials and about two dozen ambassadors, the sources said.

Among the changes in the wind: George S. Vest, ambassador to the European Economic Community and former assistant secretary for European affairs, is expected to replace Alfred L. (Roy) Atherton as director general of the Foreign Service. Atherton is retiring to become director of the Harkness Fellowships, which bring young professionals here from the United Kingdom, Australia and New Zealand. John D. Negroponte, ambassador to Honduras, would replace James L. Malone, assistant secretary in charge of oceans and international environmental and scientific affairs. Deputy Assistant Secretary L. Craig Johnstone is expected to replace Negroponte in Honduras. Richard T. McCormack, assistant secretary for economic and business affairs, is to be named to a new government post, possibly an ambassadorship in the Latin American field. An official with more economic experience, yet unnamed, would replace him. William L. Ball III, administrative assistant to Sen. John G. Tower (R-Tex.), is to replace W. Tapley Bennett as assistant secretary for legislative and intergovernmental affairs, State's chief lobbyist on Capitol Hill.

Two other changes have already been announced: veteran television newsman Bernard Kalb to replace John Hughes as department spokesman, and career diplomat Morton I. Abramowitz to replace career CIA official Hugh Montgomery as director of the Bureau of Intelligence and Research.

At least two other assistant secretaries, Elliott Abrams of the Bureau of Human Rights and Humanitarian Affairs and Gregory J. Newell of the Bureau of International Organization Affairs, may be leaving the department by spring, sources said. HAZARDOUS TO HEALTH . . .

Despite the advances of modern medicine, State Department employes and their families who work abroad still face major health hazards, said Dr. Eban H. Dustin, medical director of the State Department and Foreign Service. And, he said, they seem to be more conscious of the dangers than ever.

Dustin, who left a one-man general practice in northern New Hampshire nearly 20 years ago for the adventures of diplomatic medicine, became State's No. 1 doctor in September. He held the same job in 1979-80, before duty in Vienna.

The main changes he found in four years, Dustin said in an interview, include "much more concern with worldwide terrorism" on the part of diplomats and their families. The medical program's responses include training in disaster first aid and positioning medical supplies in places where they might be needed.

The department, he said, is also placing more emphasis on the quality of family life overseas. Today six of the 39 fulltime medical officers abroad are psychiatrists.

A decline in public health programs in some Third World nations poses new dangers to diplomats and their families. Of special concern to Dr. Martin Wolfe, State's senior specialist in tropical diseases, is the emergence of drug-resistant malaria in parts of Africa and Asia.

Polluted water and air and other environmental perils are a continuing hazard. Dr. Charles Brodine, the senior specialist in environmental health and preventive medicine, focuses on them.

Despite all these concerns, however, the No. 1 cause of death among American officials abroad continues to be accidents, especially automobile accidents, according to Dr. John Beahler, deputy director of M/Med, the State Department medical program. Wild drivers on poor roads far from good medical care is a prescription for danger in overseas living, he said.