A FEW DAYS after four local television stations carried the false news of his being "critically" shot, Mayor Barry sat at his desk at the District building and said his wife was still shaking and he was still boiling.

Across town, Marty Levin, the WRC-TV anchorman who was first on the air with the false shooting report, said he had been having difficulty sleeping and suffered personal anguish because of the incident.

Said Barry, "The more I think about it, the more angry and disgusted I get about the fact that the television station that started this out was Channel 4, and for the sake of trying to be first [they] would not check it out.

"The more I think about it, they were irresponsible, too, in the sense that reporting the news quickly could not have changed the nature of the event -- if I had been shot, five or ten minutes more [while they double-checked for accuracy] would not have gotten me unshot. Or, if I had been killed, it wouldn't have gotten me alive."

"Even more disturbing, I don't think the criticalness of what they did to the community . . . to me and my family has begun to even register. I talked to [the station manager] and he was trying to rationalize some parts of it. I said, 'You can't rationalize anything about it. Admit it was wrong and let's go about our business.'"

Essentially, Levin agrees. "Our first responsibility is to be accurate and the people here thought they were being accurate," he said. ". . . Certainly there is the pressure to do it first. But nobody would have ever said. 'This is kind of flimsy but let's go with it so we can be first.'

"But, hell, I won't rationalize it. I have no problem admitting that we blew it. It was a very, very sad mistake."

Partly as a result of Janet Cooke, the Post reporter who fabricated a story about a child drug addict, the press today is under attack as never before. A recent poll by Gallup indicates that Americans believe the most accurate, unbiased news is delivered to them in this order: network television, local television, news magazines, and -- last -- newspapers.

That hurts when you're a reporter and you know that the print media deals in detail and substance that far outdistances television news.

But if people put a lot of stock in men like Marty Levin and Jim Vance and Dan Rather, then these men have an even bigger responsibility to make sure they get it right.

The consequences of this false news could well have been tragic. When the news of the mayor's shooting first flashed in this volatile Washington summertime, I immediately thought of the riots that were triggered by the death of Martin Luther King. I was not alone. One news editor driving into work late at night said he started thinking, "Let's call the troops out because there might be a riot."

Marty Levin was all chin up when I talked with him, but his voice betrayed the tone of a man slightly convinced he is the fall guy. He's probably right. For, while it was wrong to let being first be more important than being absolutely sure, a bigger evil may have been the insane rush by other news organizations to get it on the air and over the wires next without more care.

Levin may have been wrong by trying to be first, but the other major TV stations and one wire service who followed WRC's lead don't even have that excuse.

Perhaps something good can come out of this if, as a result, the system for clearing information for the media can be improved.

The D.C. police already have a hotline to about 17 major news outlets in the city, but it's not a 24-hour service. And while Lt. Hiram Brewton, the public information officer in charge of the hotline, says he's always available at home, he also makes it clear that the police department's goals in the dissemination of news are not the same as those of the media.

"About 90 percent of the time when something happens that is newsworthy, I have to wait for a preliminary report before putting it on the hotline," he said. "We are not in a competitive business. We get the information out as soon as we can confirm it.

"Our major goal is to secure a successful prosecution in court."

It seems that lost somewhere in the middle of the media's desire for getting it first and the police goal of putting someone behind bars is the community's need to know -- quickly and accurately -- what has happened.

If the media concedes that it must be more careful, shouldn't the city also strive to provide accurate information more quickly?

In the meantime, the signal from the community is certainly clear. Everyone would rather have information late and accurate rather than early and wrong. Those of us whose job it is to inform the public have to think long and hard about how we do that in these nervous, unsettling times.