FROM THE START what has troubled even many of President Reagan's supporters--and here we are not talking of those who have simply wanted him to be tough--was a fear that he would approach the world boldly but crudely and would not bring adequate finesse to his purpose of restoring American power. One part of this anxiety has centered on Mr. Reagan's use of words, another on his use of weapons. The question has always been not just whether he was right in this judgment or that action but whether he might sweep on from a limited pronouncement or deed into something larger and more dangerous.

His speech Thurday night showed some of the familiar tendency to make statements with a potential for justifying outsized reactions. In both Lebanon and Grenada, the president said, Moscow had "assisted and encouraged the violence." Most will agree that events in once-tranquil Grenada would not have come to the point of a bloody coup without a Soviet role, although as usual the direct Soviet role is small. It is all too possible, however, to imagine extravagances of home-grown terror in Lebanon. The chronic Reagan inclination to blur the distinction between local causes and Soviet manipulation stirs unease.

At the moment--things may change--the news from Grenada may be running the president's way. Some part of the testimony of the students supports his alarm about their potential danger. The fears of Grenada's family of democracies are tending to be confirmed by the combat posture of the Cuban construction force and by the stores of arms found ashore. If Mr. Reagan cannot prove his claim that Grenada was "a Soviet-Cuban colony being readied as a major military bastion to export terror and undermine democracy," then neither can skeptics wholly ignore it.

It is powerfully disturbing, however, to find the administration reaching for findings that came to light after the intervention to justify the decision to go in. Why are we there? How long are we meant to stay? What exactly is our mission in apparently feeling we are entitled and obliged to root every fugitive Cuban out of the hills? Admiral McDonald, who is in charge of the invasion, even said he would not rule out establishing a military base. Is this policy?

In Lebanon, something else is true. To the bombing tragedies the president has reacted by raising and blurring the American stakes. He could have usefully centered on and defined the American interest in helping the Lebanese rebuild Lebanon. Instead, he allowed himself to be drawn into setting open-ended goals of establishing will and credibility in a broad anti-Soviet context.

His immediate policy, moreover, seems confused. Against whom is "justice" for the bombings to be dealt? What purpose is served by allowing anger at Syria to get in the way of the eventually unavoidable requirement to work with Damascus as the force that counts on the Arab ground? Leaving aside the matter of Israel's contribution to the American distress in Beirut, what good can come of the president's hopes in Lebanon by insisting that he is really there for the interests of Israel?

Few who saw the commander in chief on television Thursday could have failed to be moved by his tribute to the American dead. But such feelings are no substitute for sound policy. The president has the chance at least to break even in Grenada if he gets out quickly and goes on to convey that he understands the limitations as well as the uses of military power in a hemispheric setting. In Lebanon he is working in a context of terrible complexity where his primary instrument must be a diplomatic scalpel, not a club of vengeance or a blunderbuss campaign against a diffuse "communist" foe.