Back-to-back performances on the Mideast last week showed anew why Ronald Reagan and Jimmy Carter present such a melancholy choice. Each in his fashion, overdid the courting of the Jewish vote. Mr. Reagan made the usual bloopers, and Mr. Carter once again abused his office for political purposes.

Reagan's goofs have now become the hallmark of his campaign, the authentic sign that he writes his own material. His speech to the B'nai B'rith Wednesday night contained nothing so egregious as the false identification of Tuscumbia, Ala., as the birthplace of the Ku Klux Klan. Nor so foolish as questioning the Darwinian theory of evolution. Nor so controversial as calling Vietnam a "noble cause," and insisting on an "official" relationship with Taiwan.

But there was a central contradiction. Reagan singled out "negotiation between Jordon and Israel" as the key to peace in the Mideast. He invited Jordon to assimilate the Palestinian refugees. But at the same time, he dynamited conditions for such a settlement.

He blasted President Carter for selling a hundred battle tanks to Jordon -- as if King Hussein could possibly enter peace negotiations with Israel without getting a payoff for his military.

The governor also criticized the president for selling F16 jet fighters to Saudi Arabia. But Hussein will not enter the peace process without support from the Saudis, and the Saudis will not vouchsafe such support unless they also benefit from a defense buildup.

In the process of showing he did not comprehend his own proposal, Reagan also broke faith with the longstanding Republican position. The Eisenhower Doctrine legitimizes American military assistance to moderate Arab regimes.

Presidents Nixon and Ford continued the policy. Former secretary of state Henry Kissinger supported both the Jordanian and Saudi arms sales. So it can be fairly charged against Reagan that on the Mideast, as on women's rights and arms control, he is far out even by Republican standards.

Carter's abuse of office for political purposes became evident when he hid from Sen. Kennedy behind the Iranian hostages and the Soviet invasion of Afghanistan. It surfaced again in a series of national security leaks -- notably those regarding a new strategy, and a new bomber, the so-called Stealth -- both of which seemed to show the president standing up to the Russians.

Carter's speech to the B'nai B'rith Thursday was set against the accord worked out in the Mideast by Ambassador Sol M. Linowitz. Under its terms, the Egyptians and Israelis resume negotiations -- at no fixed time and with no clear agenda -- for Palestinian autonomy. In return, President Carter agrees to act as host, after the elections, to a summit meeting of President Sadat and Prime Minister Begin.

In his speech, the president held the work of Ambassador Linowitz as a kind of breakthrough. "Once again," the president said, "we have found a way to move toward peace. The talks will resume."

Actually, it was well understood that the Israelis and Egyptians would resume negotiations after the American elections, probably through a summit -- if Begin could be persuaded to come. What Linowitz did -- by emphasizing the danger of a deterioration in relations between Cairo and Jerusalem -- was make the implicit understanding explicit. Far from being a big step forward, the explicit understanding mainly tells the world that Carter is playing politics in the Mideast. If anything is achieved in the new round of talks, new concessions will have to be made to the Jordanians and Saudis to win their support for the peace process. The Israelis will dig in against those accommodations. The United States will then be obliged to hammer the Israelis -- another case of letting down a friend.

In the long run, both Reagan and Carter will have to pay a price. Reagan's errors feed a wide perception that he is not up to being president. Carter's campaign gives friends and foe alike even less reason to take him seriously as a president.

For the time being, however, the price is being paid by the American people. Our interest is in serious discussion of different problems. Instead we are being fed a steady diet of almost irrelevant charges and countercharges. The overwhelming need for some improvement underlies the importance of the debate, and provides another reason for including John Anderson.