THE TESTIMONY of Attorney General Edwin Meese III yesterday seemed to leave many people perplexed. Here was the chief legal officer of the government, and a close adviser and friend to the president, offering an account that none of his questioners could specifically contradict but that few seemed able to fully accept either. A silent battle was waged through the day over where to place the burden of proof. His questioners were demanding that Mr. Meese prove he was right, which he could not do, but Mr. Meese was in effect defying his questioners to prove that he was wrong, which they could not do. Altogether it was a strangely unsatisfying exchange, which appeared to leave people on both sides grumbling at the difficulty of establishing the truth.

The questioning centered on the dramatic weekend last November when Mr. Meese was making for the president a quick inquiry into the revelations that became the core of the Iran-contra affair. He had only a few days to make that inquiry, it is true -- but Mr. Meese, a methodical note-taking man, had nearly eight months to prepare for his testimony. Time after time, however, he said he could not recall particular events. Repeatedly it turned out he had failed to ask a question that, in retrospect, seemed urgent and unavoidable. He was, on that November weekend, looking into a sensational matter, but he brought to the hunt little of the vigilance, detachment and skepticism that one would think to be second nature on the part of a law-and-order man like the attorney general. His confidence in the integrity and candor of administration associates could be considered touching if it were not also hopelessly naive and if it had not resulted in an investigation marked by a rather laid-back quality. This is what has deprived Mr. Meese of anything like full acceptance for his claim that he was an earnest truth-seeker suddenly and unexpectedly having to deal with vast dissembling.

What Mr. Meese has said so far is consistent with the Reagan administration's depiction of itself as conscientious in policy making and alert to make corrections and inform the public once trouble came into view. Still, Mr. Meese so far is not restoring to the president any of the luster he has lost in this affair. It has to be a harmful thing to the administration that Mr. Meese is making the president's best case and that a great many people are being left perplexed by it, while others are not being left perplexed at all: they say they simply cannot believe all the things Mr. Meese is asking them to believe and they are racking the record, and their imaginations, trying to come up with a theory of what really went on.