They are specks on the map so tiny one almost needs a magnifying glass to find them. But the island ministates dotting the eastern Caribbean are the newest additions to the Carter administration's list of potentially worrisome trouble spots.

Until now, events in that area have gone virtually unnoticed as press and public attention focused on the otherside of the Caribbean, where Nicaragua's bloody civil war has prompted a top-prority U.S. campaign to force out President Anastasio Somoza and prevent a takeover by leftist guerrillas sympathetic to Cuba.

Within the administration, though, there is growing concern that the turmoil rolling the eastern islands - minuscule former British dependencies pushed into independence despite severe economic problems - could create competition between the United States and Cuba.

The roots of this concern go back to the March 13 coup that overthrew the notoriously corrupt government of Grenada and put a self-proclaimed "radical leftist" regime in control of that tiny (population 106,000) repbulic.

Grenada's new government insists that it is neither communist nor a Cuban satellite. But, in a move that sent tremors through the White House and State Department, it immediately turned to Havana for arms, military advisers and other aid.

The result was the dispatch of a U.S. envoy to deliver a protest, an angry Grenadian rejection of American "interference" - and an immediate chill on relations between Washington and the island's militant young leaders.

Since then, an island-hopping ripple effect has inspired other leftist groups throughout the eastern Caribbean to engage in labor strikes, demonstrations and other forms of confrontation with government. The escalating unrest raises fears - both in Washington and in many of the Caribbean's larger countries - that what happened in Grenada could be repeated in Dominica (population 78,000), Antigua (70,000), St. Lucia (120,000) and St. Vincent (112,00).

U.S. officials stress there is no evidence of any Cuban hand in causing the Grenada coup or in encouraging the other islands' turmoil. Conflicts building up in these places, the officials are careful to point out, stem directly from indigenous poverty over-population and social disparities.

But the officials also note that President Fidel Castro's Cuban regime has a strong interest in extending it influence throughout the Caribbean and could hardly be expected to ignore any "targets of opportunity" that might emerge from the current ferment.

Since this U.S. thinking is based primarily on scenarios of what could happen, the officials acknowledge a danger of Washington over-reacting and reverting to a Cold War mentality. In particular, they cite a need to avoid needlessly disturbing the fitful movement toward U.S. rapproachement with Cuba or giving Caribbean countries the impression that the United States wants to assert hegemony over the region.

The officials admit that the administration's reawakened interest in the Caribbean has strong "containment of Cuba" overtones. But, they add, the situation also has a more far-reaching effect - redirecting Washington's attention to the stability and well-being of an area sometimes called "America's third border."

When the Carter administration entered office, it announced that a main foreign policy goal would be priority attention for the Caribbean, and, two years ago, it sent United Nations Ambassador Andrew Young on a heavily publicized tour of the area.

Despite those good intentions, though, the administration was forced by more immediate problems in other parts of the world to put that policy on the back burner, and it has never really come to grips with the realities of the Caribbean.

In talking about the region, U.S. policymakers mean not just the string of islands stretching 2,000 miles through the Caribbean Sea between the Bahamas and Trinidad. They are referring to a larger "Caribbean basin" that includes Mexico, Central America and nothern South America.

In addition to its obvious strategic relationship to the Panama Canal and international shipping routes, the region is an important center of trade and investment, providing, among other things, two-thirds of the bauxite required by the U.S. aluminum industry and refining 25 percent of the oil entering the United States.

From another standpoint, the area's high unemployment has made it second only to Mexico as a source of illegal aliens in the United States. It also is the route across which most illegal narcotics enter the eastern half of this country.

While the countries are small, collectively they add up to a sizable bloc of votes in the United Nations and regional bodies like the Organization of American States. Some - notably Jamaica, Venezuela, Mexico and Barbados - also command considerable influence in Third World circles.

Now, the rumblings in the eastern Caribbean - coupled with the strife in Nicaragua and El Salvador on the Western flank - cause U.S. officials to worry increasingly about what some call "concentric cirles of potential trouble."

That's a reference to the possibility of upheaval producing radically inclined regimes on the smaller islands that might spread to larger countries like Jamaica, Haiti and the Dominican Republic and balkanize the region with antagonistic political and economic systems.

Noting descriptions of the Middle East and southern Asia as an "arc of crisis," one officials says: "There's not an island in the Caribbean that couldn't go the way of Grenada within five years. If you take Central America as the western point and the ministates as the eastern one, you could say we've got the potential for a 'circle of crisis' right on out doorstep."

Increasingly, such talk is heard at the highest levels of the administration. President Carter, addressing Congress June 18 after his return from the Vienna summit, cited increasing Cuban activity in the Caribbean. Secretary of State Cyrus R. Vance has said repeatedly, publicly and privately, that he intends to make the Caribbean one of his highest priorities during the year and a half that he plans to remain in office.

One key sign of Vance's interest has been the recall to active service of Philip C. Habib, who, before being sidelined by a heart attack last year, was Vance's undersecretary for political affairs and perhaps his most influential subordinate.

Habib now is returning as a special adviser and troubleshooter for Vance. Although his assignment will include three or four global crisis areas, Vance has stressed that one of the most important will be the Caribbean. The pullout by Britain, for centuries a major force, left a big vacuum.

Most of the tiny, newly independent islands among the English-speaking countries are relics of old plantation economies with glaring disparities of income and social status and a lack of resources so severe that some habitually suffer unemployment of 30 to 50 percent.

Most have been run for years by self-perpetuating political machines whose leaders have used a thin veneer of constitutionality to mask widespread repression and corruption. The most notorious of the breed was Sir Eric Gairy, the Grenada prime minister ousted by the New Jewel Movement of the new leader, Maurice Bishop.

Bishop and his cohorts, while proclaiming allegiance to Marxist-influenced theories of government and economics, insist they are not communists, Some New Jewel leaders say that if they have a model, it is not Castro but Jamaica's Prime Minister Michael Manley, who has managed to stay on cordial terms with Washington despite policies of statest economic development and antipathy to private enterprise.

In private, New Jewel leaders admit that they took arms from Castro, insisting that guns were necessary to prevent a counter-coup by Gairy, who is now in the United States. They also say they will continue to seek aid from Cuba or any other country willing to grant it with no strings attached, and would like to see the United States on the list of donors.

Washington' initial reaction, U.S. officials privately concede, was ill-advised. At the first sign of Cuban arms entering Grenada, Frank Ortiz, until recently the U.S. ambassador in Grenada, was sent to tell Bishop that the United States "would view with displeasure" a move toward military ties with Cuba.

Bishop adoitly exploited the situation by revealing the warning in a radio address and, according to U.S. sources, twisting his report of Ortiz's private message to make it sound like an overt U.S. threat against Grenada.

Washington since has approached Bishop in a more cautious and conciliatory manner, while watching to see which way events move in Grenada. U.S. officials responded with relative warmth to recent Bishop government statements about wanting better relations with the United States, but they also note warily that the number of Cuban advisers on Grenada continues to rise.

In the meantime, continuing fallout from the coup - labor strife in Dominica recently forced President Fred Degazon to leave the country - has jogged the National Security Council and the State Department's policy planners into a flurry of study of Cuba's activities and possible U.S. responses.

That planning now has gone considerably beyond the jumpy reaction that, in the immediate aftermath of the coup, caused the NSC briefly to consider slapping a naval quarantine around Grenada.

Instead, U.S. officials, while continuing to assume that Cuba will take advantage of any openings it finds in the Caribbean, also say the Cubans are moving in a prudent, low-key way that appears designed not to antagonize the United States unduly.

As a result, current U.S. planning is geared not to confrontation but to advertising a readiness to help the Caribbean countries resolve problems which, if left unchecked, could put Washington and Havana on a collision course.

In the short run, this means trying to get some money into the more volatile ministates for immediate relief of high unemployment. U.S. aid to the Caribbean during the 1980 fiscal year is expected to total about $155 million, and a big share of that is expected to go to the eastern region.

Over the longer haul, U.S. officials believe the only hope of easing the region's chronic economic instability rests in prodding the polyglot collection of former British, Spanish, French and Dutch possessions to overcome their cultural barriers and pull together in greatly accelerated regional cooperation schemes.

To encourage this, the administration plans greater stress on what one official calls "the godfather role" of the Caribbean Group for Cooperation in Economic Development. Formed at the initiative of the United States and the international lending agencies, this umbrella organization coordinates aid and induces aid-giving countries to be more active in the Caribbean.

The organization's pledges for its coming year are expected to total about $276 million. U.S. officials are encouraged that the figure is much greater than this year's $186 million and includes pledges from several new donor countries.

Even such sizable amounts are considered a mere scratch on the surface of the region's monumental problems. Administration officials insist, though, that there are "no quick and easy answers" and that integration and cooperation, fueled by increased aid, offer "the only sensible course for the Caribbean to pursue."

As one official says: "It's something that's in our interest to do even if the threat of Cuban influence turns out to have been exaggerated." But he also says, "When I listen to the rumblings down there getting louder and louder, I have to wonder whether we're coming at the problem too late with too little." CAPTION: Map, Called America's "third border," Caribbean has reawakened U.S. interest. By Richard Furno - The Washington Post