After two years of looking, American University President Richard Berendzen has appointed author-journalist Sanford J. Ungar dean of the AU School of Communication, a position he will take over Jan. 1. Ungar, who is the former cohost of National Public Radio's "All Things Considered," has most recently been a senior associate at the Carnegie Endowment for International Peace. A series on immigration issues he hosted on Chicago public television won him a 1983 Emmy.

Ungar is a former Washington Post reporter, was Washington editor for The Atlantic and managing editor of Foreign Policy magazine. His most recent book, "Africa: The People and Politics of an Emerging Continent," was published in August. He also wrote "FBI: An Uncensored Look Behind the Walls." With the appointment of Ungar, Berendzen continues his work of blending the AU academic community with social, political, official and journalistic Washington. Film Awards

The Los Angeles Film Critics Association named "Brazil," a movie unseen by American audiences, best picture of the year Saturday. The movie has been caught in a battle between its director and cowriter Terry Gilliam and Sidney Sheinberg, president of Universal Pictures' parent company, MCA. Sheinberg found the film about a man crushed by bureaucracy uncommercial and the ending downbeat. (Sheinberg should visit Washington where that's a daily story.) Gilliam trimmed the film but did not change the ending and Sheinberg took over the film, saying Gilliam had violated his contract. The film was shown in clandestine screenings to New York and Los Angeles critics and has only been seen publicly in Europe.

Other winners chosen by the film critics association, useful to consider in betting on the upcoming Academy Awards, included "Out of Africa," the Robert Redford and Meryl Streep film that opens here Friday, which was runner-up in the best picture category. The best actor award went to William Hurt for his role in "Kiss of the Spider Woman," another favorite for the Academy Award; Meryl Streep won her fourth best actress award from the group, this one for her role in "Out of Africa." Best supporting actor went to Sir John Gielgud for "Plenty" and "The Shooting Party," and best supporting actress went to Anjelica Huston for "Prizzi's Honor." End Notes

Allen H. Neuharth, chairman of the Gannett media empire and founder of USA Today, put out a press release carried by his national newspaper yesterday to deny an item in the New York Post about Rosamunda Moore, a sales assistant at The Washington Times who claimed to be his illegitimate daughter. In a terse denial under the headline "Gossip column charges denied by Neuharth," he said: "I have no illegitimate children. I do have two very legitimate and wonderful offspring, Dan, 32, and Jan, 30. Anyone else who claims any such relationship with me deserves sympathy, but should not be taken seriously" . . .

Lee Kimche McGrath, the first director of the Institute of Museum Services, an independent federal agency within the National Foundation for the Arts and Humanities, has been awarded a State Department contract to direct the Arts in Embassies Program, which makes American art available to U.S. Embassy residents in 141 countries . . .

The Space Shuttle Columbia may have a difficult time getting off the ground tomorrow with Rep. Bill Nelson on board. Nelson, the second member of Congress to go into outer space, is taking a few things with him, including the banners of his alma maters, Yale University and the University of Virginia Law School, a U.Va. bumper sticker and T-shirt, banners from several colleges in his Florida home district, the seal from his home town of Malabar, Fla., and one of Speaker Tip O'Neill's gavels . . .

If you've heard the theme song from "The Beverly Hillbillies," or from television's old "77 Sunset Strip," around the offices of the House and Senate judiciary committees, you haven't been imagining things. The Songwriters Guild has been lobbying on Capitol Hill. It seems that legislation has been introduced that, through a complex formula, will reduce the amount of residual compensation the composers of television theme and background music would receive. So guild president George David Weiss has delivered cassettes with 65 familiar television musical themes from the golden 1950s and 1960s. He figures that the Congress members will be so awash in nostalgia they couldn't do anything but oppose any proposal that might sully the memory of "Green Acres," "Mr. Ed" or "Dobie Gillis" . . .