The bush-league quality of the administration's approach to the diplomacy finds new expression in the most recent trip to the Mideast by Secretary of State Cyrus Vance. Vance went without a clear idea of what he could achieve or how.

He had to grasp at straws, and in the process caused a couple of interesting proposals to be shot down. He has returned with prospects for a settlement not advanced - nor likely to be by the administration's latest device of arranging for foreign ministers to meet with President Carter after the United Nations General Assembly convenes next month.

As many of us sensed at the time, the mission began under poor auspices. The Israelis were on guard against any move to slip the Palestine Liberation Organization into negotiations. They have been that way ever since President Carter, speaking to a town meeting at Clinton, Mass., in March, put the hardest problem of all - a homeland for the Palestinians - at the top of the Mideast agenda.

The Arabs for their part were aquiver with suspicion of moves to exclude the Palestinians from negotiations. They were put in that position when President Carter gave a warm reception to the new Israeli prime minister, Menachem Begin, during the state visit despite Begin's adamant refusal to deal with PLO leaders.

The best that could be hoped for, in these conditions, was that Secretary Vance could maintain some momentum for continuing negotiations that might eventually lead to a Geneva conference. But to do that he needed a clearly defined plan of action. Instead, he left impelled by nothing but the President's optimism. He was thus obliged to go all out for every opening that presented itself.

One opening came on the first stop of the trip. In Egypt, President Anwar Sadat talked, as he had many times before, about a pre-Geneva meeting of "working groups." Vance allowed that idea to be associated with a notion of his own about talks among the foreign ministers at the United Nations General Assembly. Begin immediately sensed a way to cut out the Palestinians and hailed the idea.

Begin's support made it seem that a full-scale effort to exclude the Palestinians was under way. So in Syria, the next stop after Egypt, President Hafez Assad, feeling obliged to show that he was not selling out the Palestinians, shot down the idea of pre-Geneva working parties.

With one good notion down, the Vance party immediately floated another. In Saudi Arabia, the next stop after Syria. word was put out that the PLO was considering a plan to accept, with slight modifications, U.N. Resolution 242. Since the resolution speaks of "secure borders" for Israel, acceptance could be construed as a step toward recognition of the Jewish state. President Carter, speaking from Plains, indicated that if the PLO took such a step, the way would be open for their participation in the Mideast negotiations.

Begin inevitably saw that idea as a maneuver for smuggling the Palestinians into the talks. In an extraordinary toast, he likened the PLO to the appeaser who sold out the Jews to Hitler.

Begin's reiterated refusal to deal with the PLO immediately caused a hardening in that quarter. A PLO meeting scheduled for this week to move on Resolution 242 was postponed. The PLO leader, Yasser Arafat, said the question would have to be decided by "Palestinian rifles."

Thus, premature publicity killed two procedural suggestions that might reasonably have been tested in private talks. The President and the Secretary now have to start all over again in meeting with the foreign ministers when they visit the U.N.

Which is worse than no progress. For the second time, the first being his visit to Moscow, Vance has returned empty-handed from a highly publicized foreign visit. The whole world has seen that the President is continually sending his chief negotiator abroad on missions impossible, and it is clear that Vance needs to delegate more of the traveling to deputies.

In the Mideast, however, the difficulty is more serious. Carter came to office convinced that the right approach was a comprehensive settlement. Circumstances have changed dramatically since then - if only because of the accession of Begin to power. But Carter has not rethought - he has not even allowed himself time to rethink - his strategy. So he keeps hurling his administration up against the realities with results that are all too visible.