THE CHRISTMAS SHOW at Radio City Music Hall opened over the weekend, with the traditional production numbers, special effects, fabulous costumes, live animals, and, of course, the Rockettes. Audiences are expected to exceed 700,000 before the show closes Jan. 8. LIONEL RICHIE went ``multiplatinum'' with his album ``Dancing on the Ceiling,'' which became the first ever to exceed gold, platinum, double platinum, and triple platinum status on the same day, since the Recording Industry Association of America introduced the ``multi'' designation two years ago. THE SMITHSONIAN INSTITUTION will buy Folkways Records, a label known for its international collection of ethnic and folk performance. Terms of the agreement include a guarantee that the Smithsonian will keep the existing 2,200 titles available on vinyl and tape and will continue to release new discs. THE PARENTS RESOURCE MUSIC CENTER and representatives of the recording industry will meet soon to assess the one-year ``trial period,'' during which the industry has voluntarily labeled records whose lyrics might be considered pornographic or otherwise offensive. The parents' group hopes to close some loopholes in the labeling process. MARTIN SCORSESE AND WALT DISNEY PICTURES will collaborate for the next two years. The director and the studio - pleased with the success of their first picture, ``The Color of Money'' - have signed an agreement under which Scorsese will produce and direct an unspecified number of films for the studio. SPORTS ILLUSTRATED AND HBO plan to market home video cassettes, beginning next summer, on such themes as great moments in sports history and preseason team previews.