THE NATIONAL Gallery continues with its "Cinema of the American Avant-Garde: A Retrospective View" Saturday at 2 in the East Building Auditorium. Screening this weekend are Larry Jordan's Duo Concertantes and Our Lady of the Sphere; Robert Breer's Jamestown Baloos, as well as his 66, 69, 70, Gulls and Buoys and Fuji; and Harry Smith's Heaven and Earth Magic Feature. All films are 10 minutes or less, except for the 66-minute "Heaven and Earth." Call 737-4215.

This week, at the Library of Congress' Mary Pickford Theater (James Madison Building, third floor), it's Victor Schertzinger's Something to Sing About (1937) Friday and Monday at 7:30, with James Cagney playing a not-so-great hoofer who makes it anyway. Russell Mack's Once in a Lifetime (1932), adapted from the play by Moss Hart and George S. Kaufman, is shown Tuesday and Wednesday, also at 7:30. The films are part of the Library's three-month series, "Hollywood's Hollywood" -- films where Hollywood does Hollywood. Coming up in that series are King Vidor's Show People (1928), Elia Kazan's The Last Tycoon (1976), John Schlesinger's The Day of the Locust (1975), Singin' in the Rain (1952) and Blake Edward's S.O.B. (1981). Admission is free. Reservations must be made. Call 287-5677.

Also this week, the Biograph will show Washington's first commercial run of Peter Greenaway's brilliant study in symmetry, A Zed and Two Noughts, for three days only (Tuesday through Thursday). The rest of the week (and through February 8), it will show Heinz Schirk's The Wannsee Conference, a dramatic, word-for-word reenactment of the infamous 1942 Nazi meeting in Berlin, in which the "final solution" of the Jews was discussed over brandy and sandwiches.

The Hirshhorn Museum begins its winter film series this week and, as always, the films are thoughtfully chosen, provocative and free. Thursday at noon, it's Sol LeWitt, a 1977 video profile of the abstract artist. At 8, it's "Animation in the U.K," a selection of shorts (not children's fare) from the 1987 London Film Festival. Some of the films include Ian Andrew's Dolphins, an underwater mood piece on the mammals, and Aidan Hickey's An Inside Job, which Hirshhorn programmer Kelly Gordon describes as "The best film on terror at the dentist's since Steve Martin in Little Shop of Horrors." Binky and Boo, by Phil Austin and Derek Hayes, is a "dark, grim, manic" film about two clowns who remember apparent performances before strange audiences through the ages, including Caligula and Hitler. And in Andrew Staveley's Strangers in Paradise, Gordon explains, people resembling "shoppers from another planet scurry and browse in this phantasmagorical miasma . . ." Got that? The British show is repeated the following evening (next Friday) at 8. Call 357-2700.