It will probably bring tears to the eyes of many of those Northwest Washington Volvo liberals worrying about getting their kids in private schools or into the right colleges when Peter, Paul and Mary are arrested next week at the South African Embassy and are led away to a metropolitan police van while singing "We Shall Overcome." It's been a long time since the anthem singers of the 1960s have been so closely identified with a cause as they were during the civil rights and anti-Vietnam war demonstrations.

If all goes as planned, the famous trio will be out near the South African Embassy Wednesday when a freedom letter is presented to Nobel Peace Prize winner Bishop Desmond Tutu, who will be in town. The letter will contain thousands of signatures expressing opposition to South Africa's apartheid policies. After that the singing group will walk to the embassy door to be arrested. Singer Mary Travers plans to be arrested with her daughter Elicia, 19, and her 68-year-old mother Virginia Coigney. Peter Yarrow will be there with his daughter Elizabeth, 15. Noel (Paul) Stookey plans to be arrested alone.

Next month there will be a 25th-anniversary tribute to Peter, Paul and Mary at the Kennedy Center, sponsored by the Free South Africa movement. Among the guests expected for that tribute are singers Judy Collins, Odetta, Carly Simon and John Denver, actor Lou Gossett Jr., former assistant secretary of state for human rights Patt Derian, activists Gloria Steinem, Coretta Scott King and Cesar Chavez and Transafrica executive director Randall Robinson. Sheen on 'Snyder' Movie

Martin Sheen is known as an actor who is not easy to get along with and as a man with strong personal opinions. He hasn't even started the made-for-TV movie about hunger and homeless activist Mitch Snyder and he is dissatisfied with the script. Sheen was Snyder's personal choice for the role, and Snyder argued with him to take the part after Sheen had turned down the script.

In an interview on the "CBS Morning News" yesterday, Sheen said that "in its present form, the script avoids criticizing anyone in the administration, particularly the president . . . If he Reagan were to show any interest in the homeless via visiting a shelter or even inviting one homeless person to the White House for a bite to eat and a chance to warm up, you can imagine the effect on the consciousness of our country."

Sheen said that in spite of his misgivings he changed his mind after a long conversation with Snyder, who reminded him of Mother Teresa's advice: "If you have food for only one and you're facing a million starving people, feed the one." Snyder pointed out during the same interview that he agreed to the movie with "minimal expectations," but hoped the film would give people a deeper understanding about street people. End Notes

The Washingtonian magazine finished 1985 ranking second in the nation among city magazines for the largest number of advertising pages. In first place is L.A. Magazine. This is the first time the Washingtonian was able to nudge out San Diego Magazine, which traditionally has held the No. 2 slot . . .

The New York Times has nominated author and Daily News columnist Ken Auletta for the Pulitzer Prize. Daily News columnist Liz Smith reported yesterday that Auletta was being nominated for his two-part article that appeared in the Times magazine on the fall of the financial house of Lehman. The series, which The Times syndicated, grew into Auletta's new book "Greed and Glory on Wall Street." Auletta, who is under contract to write a weekly column for the Daily News, said yesterday he was "thrilled" and felt especially honored because it is so unusual to have one newspaper nominate someone who is more identified with a competing paper . . .

That's one way to spend New Year's Eve . . . Delaware Rep. Thomas R. Carper was married to Martha Ann Stacy just after midnight on New Year's Eve in Wilmington, Del. . . .

Hotel and fire rescue officials are refusing to comment on the matter, but troubled singer Connie Francis was removed from the Grand Bay Hotel in Miami and placed in the Miami Mental Health Center. Center officials would not reveal whether the singer had been released, admitted or transferred . . .