"Reagan Calls Case Closed on Haig Departure" read the banner across page one of The Post's late editions July 1. It was plainly drawn from the lead story by White House correspondent Lou Cannon, which quoted Mr. Reagan as asserting this at a press conference the evening before. Well, the president didn't so assert. In response to a question from the Christian Science Monitor's Godfrey Sperling, "Is the case closed?" Mr. Reagan replied, "You bet. That case is closed." He and the reporter were talking about the case of incumbent Secretary of Labor Donovan, not former secretary of state Alexander Haig. A separate story on Mr. Donovan with "case closed" in its correct context was run on an inside page.

This piece is about the paper's failure to correct a prominent error. The decision not to--after it had been recommended by several--was taken by executive editor Ben Bradlee, who now acknowledges it was a mistake. Initially, Mr. Bradlee says, he felt that the president's unresponsiveness elsewhere in the press conference--refusing twice to elaborate on his acceptance of Mr. Haig's resignation--had the "effect of closing" the Haig case. While, it seems to me, that is inadequate, it may not be irrelevant.

It was, in fact, Mr. Cannon who returned to the subject after Mr. Reagan had dismissed an earlier question: Don't you think that the American people deserve to know more . . . ?" he asked. "Lou," the president answered, "if I thought there was . . . I would be frank and tell them." Mr. Cannon took one more run at it, but met the same stone wall. End of subject by presidential command.

The error, oddly enough, did not occur in the early editions of The Post, which go to about 100,000 subscribers. That headline read: "Reagan: Nothing Further to Disclose on Haig." The story, also by Mr. Cannon, said, "President Reagan told a nationally televised press conference last night he does not believe it would 'benefit the people' to know anything more about last week's resignation of Secretary of State Alexander Haig." Nothing about "case closed." The piece went on expertly to summarize highlights of the conference.

Making no excuse for the later error, which, regrettably, went to several hundred thousand readers, the process involved in reporting a late evening news conference against deadlines is informative. In this case, Mr. Cannon dictated the first-edition story before leaving the White House. The front page was held open for him. Meantime, the editors had chosen to break the total coverage of the conference into three more detailed stories for the "late city" edition. Mr. Cannon returned to the office to write the foreign policy story--1,000 words-- against the next deadline.

He admits straightforwardly to a lapse in putting "case closed" into the lead of the later story, understandably attributing it to deadline pressure, the president's clear determination to say nothing further about Mr. Haig and to the fact the phrase was uttered.

Not so understandable is how the error got by the editors, at least two of whom watched the conference on television and who called for the stories for the final editions. Other than "things like this happen," no better explanation was available for the record. It is a fact though that editors simply don't anticipate mistakes in the copy of first- rate reporters such as Mr. Cannon. In this instance, his story for the first edition provided a sure marker. The editors were giving more attention to stories by two other reporters on other news from the press conference.

Most parties, including this one, recommended a correction be published the next day. It would have been as simple and as necessary as a correction in another newspaper some years ago: "That was the sun in yesterday's picture, not the moon."

Failure to print a correction leaves the paper with an incorrect record of a presidential statement and the risk that someone going to the news clips a year from now could repeat the mistake. As of today, The Post library has not received a correction for the file, although I was told such a correction should be standard operating procedure.

Last, and to ride a favorite horse of mine, the newspaper ought to carry more text from presidential press conferences and other newsworthy pronouncements. Then you have exactly "what the man said." This case should provide more incentive.