THE MATTER OF the United States' leaving UNESCO is current again, because just a year ago the Reagan administration said it would pull out at the end of calendar 1984 if the politicization and mismanagement rampant at the U.N. Educational, Scientific and Cultural Organization were not halted. So have they been halted? It's not an open or shut question. In the view of some of the closest observers, things are better but not conclusively better. The argument has shifted to whether they can still improve and, specifically, whether they can improve while UNESCO remains under Amadou Mahtar M'Bow, the man from Senegal whose leadership style is at the heart of the UNESCO dispute.

Recently official American relations with the agency got even worse. The State Department official most identified with pulling the United States out, Gregory Newell, accused its secretariat of being "disdainful" of American sensibilities on key free-press issues, and charged Mr. M'Bow with a "breach of the promises" he had made to Washington on that score. Other administration appointees at the same time have been trying to maintain the access and presence required to push for the agency's reform. President Reagan is being advised that he cannot be seen to have lightly made a warning of withdrawal but also to keep plugging for reform. He is also being counseled to keep in step with America's allies, so that the United States will not get out alone.

The latest event in the UNESCO imbroglio is an announcement by Britain that it will join the United States in pulling out unless the agency makes further management and budgetary reforms. A year's notice is required, however, so British withdrawal would not take place until the end of 1985. This possibility has led to a new proposal by Rep. James Scheuer, whose pursuit of UNESCO reform -- and not so incidentally, Mr. M'Bow's continuation in his job -- has been dogged. He would have the United States consider delaying its withdrawal by a year in order to fall in with Britain and the other European countries that may follow its lead. The group of them contribute more than half of UNESCO's budget, and, together, they could have a major impact, especially if they worked with Third World moderates who wish to preserve the organization in a form useful to them. It's worth thinking about, anyway.