Sometime carpenter Jimmy Carter and his wife Rosalynn led some 500 people yesterday on the first leg of a 1,000-mile walk from Americus, Ga., to Kansas City, Mo., to raise money to build houses for the poor. "I'm just going to walk nine miles, almost 10 miles, with you today," the former president explained. "This walk shows the dedication of leaders for Habitat for Humanity all over the world who hope to raise a million dollars." Carter plans to meet the group at the completion of the walk in Kansas City on Sept. 18.

The Carters are strong supporters of Habitat for Humanity program and for the past two years have worked on rehabilitation projects in New York City. The hoped-for $1 million will go to the poor in interest-free loans to buy materials for houses. Habitat's volunteers help the loan recipients build their own homes. Among the small group on the trek are representatives from as far away as New Guinea and India. The High Cost of Eating

Things are tough on Embassy Row, where at one time some foreign governments paid their representatives tropical-duty pay for enduring Washington's heavy, muggy summers. Now, however, they have an argument about the high cost of living here. After yesterday's front-page story reported that Washington grocery prices are the highest in the continental United States, calls came in from the World Bank as well as the embassies of West Germany and Austria. The callers seemed to see a good possibility of using the information about the high cost of food in Washington to argue back home for an increase in living allowances. Navi Naisoro, executive director of the World Bank, said his staff believes that the envoys here are in a good position to argue for more money. Out and About

Guru Bhagwan Shree Rajneesh, nine months of travel and a number of countries later, returned to India yesterday after being unable to find any country that wanted him. The 54-year-old guru was forced to leave the United States last November after pleading guilty to charges of arranging sham marriages at his Oregon commune to help foreign followers remain there. He arrived in Bombay in green robes and wearing a diamond-studded headband. Over the past months he has been in such countries as Nepal, Greece, Uruguay and Cyprus in search of a land to establish a commune for followers. He said he would be in India for a few months but didn't say if he planned to stay or if he was welcome there . . .

The opening session of yesterday's Senate Judiciary Committee hearings into the nomination of Justice William H. Rehnquist to head the Supreme Court was routine. The press was not paying much attention as John Lane of the American Bar Association was testifying on the nomination in the morning. Then a television crew member whispered into the ear of Westinghouse Broadcasting reporter Patricia Sagon. She looked under her chair and, seeing a small, gray mouse, let out a yelp and darted away. The equally frightened mouse ran into the audience but no one seemed to notice. Apparently the audience was mesmerized by the testimony . . .

Hospital Report: Singer-songwriter Paul Davis was hospitalized in critical condition yesterday after being shot in the stomach during a robbery attempt outside his hotel in Nashville. Police said Davis, whose credits include "Ride 'em Cowboy" and "I Go Crazy," was in the intensive care unit at Vanderbilt University Medical Center . . . Ella Fitzgerald returned home to Los Angeles yesterday after her stay at Niagara Falls Memorial Medical Center in New York, where she was admitted Sunday morning suffering from congestive heart failure, a weakening of the heart. While at the hospital the great jazz singer received a telegram from President and Nancy Reagan and telephone calls from fellow singers Frank Sinatra, Stevie Wonder, Pearl Bailey and Lena Horne as well as composer Henry Mancini . . .

Several members of the British Parliament expressed outrage yesterday at what they termed the "laughable" $370 fine assessed to singer Boy George for using heroin. One said he should have been jailed. The magistrate said the fine was light because Boy George, lead singer of Culture Club, was getting treatment to help kick the habit. One politician pointed out, however, that American actor Stacy Keach served six months in jail for smuggling cocaine into the country and that British-born actress Judy Carne was given a three-month sentence for bringing drugs in from the United States. Another member of Parliament said the sentence "makes a mockery of police efforts to eliminate drugs. It is not a deterrent -- it could even be classified as encouragement" . . .