THE THIRD Reagan-Gorbachev summit ended in something less than total cheers and hurrahs. That's probably just as well. A valuable missile treaty years in the making was signed as scheduled; although Mr. Gorbachev reported ''some headway'' in reducing strategic arms, the work done on regional disputes and on human rights fell short of producing accord. No one who observed the lurches last year at Reykjavik, however, would argue that summits are necessarily the right place for bold negotiating breakthroughs. All over town Mr. Gorbachev displayed his wit and high-powered energy, but, we surmise, not too many people took this display as the last word on the summit. By the end of the three days, it seemed that contacts between the leaders had been extended, issues clarified and impetus given to a search for ways to ease the real differences between the two countries. That's plenty.
It was not so long ago that the Soviet press was portraying Mr. Reagan as a new Hitler. This image yielded to Mr. Gorbachev's decision to seek out the American president as an interlocutor, the better to allow him to tend to his country's sizable domestic cares. On his part, Mr. Reagan added to his instinctive aversion to communism a pragmatic view permitting him to seek common ground on practical political concerns. But whether their relationship now has a special chemistry to it, as some on both sides (on rather flimsy evidence) were at one point suggesting, is less important than that they had the opportunity to come to a clearer view of the other's goals and limits. A clearer view would help them pursue understandings of mutual advantage. It should also show them where further agreements will be hard to come by. Both leaders use words such as ''true peace'' and ''good peace'' to describe their aims. But nothing in their shared national experiences suggests that all differences between their countries are artificial, accidental, unnatural, soluble -- far from it. The right Soviet-American goal remains to reduce the costs and perils of a difficult, adversarial relationship.
The point is tellingly illustrated by Mr. Gorbachev's continuing inability to grasp the broadly held American view that a prime purpose of a better relationship is to see the Soviet Union put into practice its commitments on emigration and human rights. Evidently he had thought some lesser gestures and an emphasis on arms control and peace would ease the pressure on this front. When it did not he responded sharply and in some instances bizarrely, as in his suggestion that Moscow in limiting Jewish emigration does only what Washington does in limiting Mexican immigration. By opening himself to a good range of American opinion on this and other issues, however, Mr. Gorbachev used the summit well. Presumably he will carry his findings back to the Politburo. We hope that, on a return trip, he does more business and continues his education, and that Mr. Reagan does the same when he goes to Moscow next spring.