A mickey Mouse watch sits in a glass case in the Library of Congress, one floor below the Gutenberg Bible; a short stroll away from the precious Stradivari instruments which are also in glass cases. Besides the watch is a fountain pen that used to belong to Walt Disney, and on a nearby wall is a 1917 Disney drawing that gives no clue that the artist might develop into a specialized kind of genius.

They are part of an unusual exhibit which opened yesterday, entitled: "Fifty Years of Animation: Building a Better Mouse," and comprising 120-plus items associated with the oeuvre of Walt Disney - everything from comic strips and pop-up children's books to the manuscript score of Leopold Stokowski's orchestration of "Night on Bald Mountain" for "Fantasia."

Between now and Feb. 28, when it will close, the "Better Mouse" promises to be the most popular free show in a part of town that includes such three-ring attractions as the Smithsonian, the Supreme Court and the House of Representatives. The reason for this popularity is not primarily the Disney-related books and drawings and paintings, attractive as they are, but eight video screens set cozily into the library's marble walls on which you can watch:

Two little pigs singing "Who's Afraid of the Big Bad Wolf" (the third is too busy laying bricks to join in the harmony).

Pinocchio and Papa Geppetto having a tear-filled reunion somewhere in the intestines of Monstro the Whale.

Bambi, learning that fawns do not navigate easily on ice despite Thumper the rabbit's assurance that "It's all right - look; the water's stiff!"

Mushrooms and ostriches dancing to the music of Tchaikovsky and Ponchielli.

The "Pink Elephants on Parade" sequence from "Dumbo," in which surrealism becomes a form of mass entertainment.

Each of the eight screens shows a film clip lasting three or four minutes, and taken together they give a panoramic view of Disney's art from "Steamboat Willie" (1928), the first cartoon animated to synchronize with a soundtrack, to "Bambi" (1942), which marked the technical high point of his studio's output.These films, the exhibit's catalogue says, "are still the yardstick by which all other character animation must be measured."

A second opening will be held for children on Friday, a school holiday, with guest appearances by Mickey Mouse, Goofy and Pluto.

The exhibit, which cost the Library of Congress $35,000 to mount, was assembled in cooperation with the Disney Studio, but most of the material exhibited was already in the library's collection - including, for example, a map of Never-Never Land acquired by the library's Geography and Map Division soon after the opening of "Peter Pan."

"This exhibit is our answer to King Tut," a library spokesman said. "We expect a lot of people to come see it, and we're going to send it traveling next summer. We are trying, among other things, to establish the point that the Libarary of Congress has a very diversified collection - not only the Guterberg Bible and books and manuscripts in every language you can think of, but films, recordings, sheet music, posters and cartoons. We have also wanted to do an exhibit on the history of cartoon animation, and Walt Disney's work is the most important part of that history." CAPTION: Illustration, From "Building a Better Mouse," above, and Walt Disney with Mickey, below, Copyright (c) 1935, Walt Disney Productions; Picture 1, From "Building a Better Mouse," Copyright (c) 1933, Walt Disney Productions; Picture 2, Pastel sketch of Timothy Mouse from "Dumbo," Copyright (c) 1941, Walt Disney Productions; Picture 3, no caption