The problem wasn't opposition to the idea of Strategic Defense Initiative lasers blasting enemy missiles out of space; it wasn't complaints that a country that can't get the B1 bomber flying right is going to have a hard time zapping Soviet warheads with particle beams in an outer-space skeet shoot; it wasn't worries that a stock market crash will keep us from spending billions to acquire the SDI system that President Reagan proposed in 1983.

No. For those at last night's screening of a new half-hour film about SDI produced by the American Defense Preparedness Association, the problem was described best by Secretary of Defense Caspar Weinberger, who said: "Most Americans believe we already have a strategic defense system."

Who can blame them? Mikhail Gorbachev backs out of a Washington summit meeting because of our SDI. We've been talking about it for four years, ever since Reagan proposed it. It has required a reinterpretation of the 1972 antiballistic missile treaty with the Russians. And it even has a nickname.

"They sneer at it by calling it 'Star Wars,' and unwittingly hand the Soviets a propaganda tool," Weinberger said in a speech before the movie went on in a hotel ballroom full of defense contractors, congressional aides, young staffers from the White House and the Defense Department, and a sprinkling of journalists.

Nevertheless, SDI does not exist yet, at least as a way of shooting down missiles. Hence this film, titled "SDI: The Prospect for Peace" and made by ADPA, a defense lobby and educational group largely funded by defense contractors.

The film follows in a long screen tradition of concern about nuclear war. We've been watching one version or another for 30 or 40 years, it seems. The little kids on the playground, the radio alert, people looking skyward, the blinding flash, the mushroom cloud.

Atomic anxiety has ebbed and flowed since we dropped two bombs on Japan in 1945. Our early horror at nuclear destruction dwindled until a revival of horror at our hydrogen bomb tests in the Pacific -- tests that killed Japanese fishermen and forced the evacuation of islanders. We worried about strontium 90 in our milk, we tuned into radio alerts on CONELRAD, and in a film for schoolchildren, Bert the Turtle taught kids to "duck and cover."

After the Cuban missile crisis in 1962, fears eased. In 1959, two-thirds of Americans said the threat of nuclear war was our biggest problem. Five years later, only a sixth said so. There were fears when India exploded its "nuclear device" in 1974, and environmentalists used the image of the cooling towers at Three Mile Island, site of a nuclear reactor accident in 1979, to campaign against nuclear power. The election of Ronald Reagan to the presidency renewed fears of nuclear war, and now with the imminent Soviet-U.S. treaty on shorter range missiles and the certainty of a new president by 1989, fears may be ebbing again.

"President Reagan couldn't be with us tonight -- he had some higher priorities with the economy," said Lawrence F. Skibbie, head of ADPA. Then he showed a videotape of the president calling the SDI film "one of the most important -- and informative -- documentaries ever made."

After the scene in the playground, the film eschewed more horrible conventions of movies about nuclear weapons -- no Japanese burn victims, no rubble, none of the porno-violence of talking about just how far you can be from a drop site and still have a piece of a plate glass window driven through your neck.

Instead, lots of missiles rise into the air, lots of officials talk at the camera, lots of clouds go mushrooming up. It has the high, gentle, measured, creamy tone of a lot of corporate propaganda, like Merrill Lynch defending the virtues of the stock market, or a tobacco company asking us to think about smokers' rights. It has none of the hysteria of the television movie "The Day After" and none of the cheerleading of Daniel Graham's High Frontier campaign that grabbed attention for SDI a number of years ago.

The premise is established in three interviews near the beginning of the film. Three Americans say they thought we already had a strategic defense of some kind.

"As far as I know we have our own defensive weapons," a woman says. How mysterious! Before the fact, did anyone think we'd already landed a man on the moon? Cured yellow fever?

Asked about this peculiar delusion, Kenneth Adelman, director of the U.S. Arms Control and Disarmament Agency, said, "When I go around the country, people can't believe that we don't have a defense system."

The movie left it unclear exactly what we do have. The most dramatic demonstration of SDI's potential showed a chemical laser at White Sands, N.M., knocking apart a grounded Titan missile in the manner of a .22 rifle knocking down a stack of tin cans. It invoked the miraculous history of science, it gave SDI opponents their chance to argue their case, and it wound up with those children out on the playground again.

ADPA has distributed the film to every member of Congress and to program directors at television stations across the country. The United States Information Agency will distribute it overseas. Washingtonians will get a look at it on Channel 7, Sunday, Nov. 1, at 2:30 p.m.

Donald A. Hicks, a former aerospace executive and undersecretary of defense, said after the screening: "I think they're trying to find ways of still keeping public support, while downplaying the short-term benefits of SDI."

Then again, why worry about short-term benefits when people think we've already got SDI?