IN HIS ecological message to Congress on Oct. 2, 1965, Lyndon B. Johnson said: "I pledge you we are going to reopen the Potomac for swimming by 1975." Coincidentally, perhaps too coincidentally, Chairman Mao dogpaddled down the Yangtze at the head of his Politburo.

If the Chinese still can swim the Yangtze, Washingtonians still cannot swim, wade, dive or water ski in the Potomac, the Anacostia, the Washington Ship Channel, Rock Creek, Oxon Run and their tributaries because of Regulation 71-28 enacted Aug. 27, 1971, by the D.C. City Council.

Never rescinded, never amended and never truly enforced, that regulation indicts the river for carrying "extraordinarily high levels of pollutants from human and animal waste," which contain bacteria such as "salmonella and hepatitis, and viruses." According to Regulation 71-28, George Washington's river has become a gurgling cesspool, a threat even to frisky dogs. To illustrate:

A dog day in August, a picnic at Fletcher's Boat House, the National Park Service's riverside concession. Rover dashed into the water, leaves it, shakes himself. Droplets fall on your family. You are subject to a fine of up to $300 unless you "cleanse" Rover and all those whom Rover sprayed because:

Sec. 8, sub (d): Any person who contacts the waters designated as a public health hazard in this Regulation shall as soon as possible after that contact cleanse himself over the area of contact.

Sec. 8, (e): Any person who owns or supervises or otherwise controls an animal which contacts the waters designated as a public health hazard in this Regulation shall cleanse such animal as soon as possible . . .

That the District's Bureau of Air and Water Quality Control, the National Park Service, the Potomac Bassmasters, Maine Avenue fishmongers, thousands of picnickers, canoeists and fishermen don not share the Regulation's subdued hysteria is fortunate, for neither Fletcher's nor the Washington Canoe Club nor Swain's Lock operates pet-cleansing facilities.

To inject a note of reality, the City Council's Transportation and Environmental Affairs Committee has scheduled a June 29 public hearing to help answer the question: "How Clean Should the Potomac River Be?" Desired degress of future cleanliness cannot be debated without knowing the river's current cleanliness. Items:

According to John Brink, director of the D.C. Bureau of Air and Water Quality Contol, "The river is probably cleaner than an any time during our lives."

According to a well-known Georgetown ecology professor who preferred to remain anonymous: "There are places where I wouldn't put my arm in it."

According to criteria published by the U.S. Environmental Protection Agency, the Potomac is too contaminated to permit boating much less swimming or fishing.

Paradoxically, all three appear to be correct.

Brink bases his conclusion on countless river samples collected, analyzed and plotted since the early 1960s and on a lifetime of observing the water. The Georgetown University ecologist focuses on discharge points for untreated sewage; such sewage is laden with viruses which, unlike fecal bacteria, can sometimes penetrate human skin. EPA criteria frequently are founded on "worst case" analyses, thus providing the public a margin for safety. After subjective considerations are shed, however, these truisms remain:

1. The Potomac River is cleaner now than it was 15 years ago, judged by the kinds of pollutants measured by the District. After the Blue Plains treatment plant began chlorinating its effluent, the coliform count there dropped more than 90 per cent in seven years.

What's coliform? In the gut of every warm-blooded animal live billions of bacteria, harmless themselves, shed through the feces. Coliform bacteria, therefore, are a yardstick of fecal contamination and were the culprits that forced the shutdown of the $160,000 Lady Bird Johnson fountain on Hains Point. It was misting passers-by with fecal bacteria.

According to medicine's standard Textbook of Microbiology, "when water is polluted with human fecal material, it is probable that it contains bacteria which cause enteric infection." Among such bacteria are pathogens responsiblefor paratyphoid, typhoid, dysentery, cholera, intestinal capillariasis and a variety of worm-related diseases. Unlike harmful heavy metals, chemicals and viruses, such pathogens do not lodge in the cells and tissues of fish. As a local gastroenterologist put it, "horses are full of tetanus but you don't catch tetanus from a horse."

2. The amount of dissolved oxygen in the river is climbing, even where pollution is notorious. Dissolved oxygen is desirable for two basic reasons: It preserves the aesthetics of a river, in effect deodorizing it, disinfecting it from green-scumalgal blooms; and dissolved oxygen supports aquatic life, spawning generations of perch and herring, gamefish such as trout and bass, and their own smaller food fish. Thus modern sewage treatment plants work to rid effluents of oxygen-demanding molecules.

So successful has Great Britain's Thames River cleanup proven that the first salmon in 141 years, the first since 1884 when Britain abolished slavery, was caught in 1975 off London. That fish is mounted now in a national museum. Here, dissolved oxygen has enabled rockfish to ascend the Potomac almost to Chain Bridge and largemouth bass to descend at least as far as the Navy Yard.

3. The Potomac remains in violation of criteria published by the District. In its latest reportto the City Council, the Department of Environmental Services states that the fecal coliform count above Key Bridge violated standards during each month of 1976. "In summary," says the report, "the Potomac and Anacostia Rivers do not meet the fecal coliform standards for either water contactor-or nonwater contact (boating) recreation."

The D.C. government, therefore, is subsidizing a host of activities which, if not quite illegal, are beyond the spirit of the law. Canoeing, hydrofoil racing, fishing from rowboats, scenic cruises of the Wilson Line, all of the Washington marinas and Presidential yachts (if any existed.)

An insoluble conundrum? No, under federal water quality legislation, local political entities may set their own standards. To enfranchise boating, Washington need only lower those now in effect.

But a genuine cleanup of the Potomac poses monumental problems, one political, three practical.

The political problem is one familiar to Washington - Overlapping jurisdictions. As the Potomac flows 287 miles from Hampshire County, W. Va., to the Chesapeake, it touches Virginia, Maryland, the District, the Council of Governments, the Interstate Commission on the Potomac River Basin, the Potomac River Basin Advisory Commission, the National Park Service, the Environmental Protection Agency, the House Public Works Committee, the Department of Transportation, the Army Corps of Engineers, their constituencies, priorities and budgets. Obtaining the consent of all or even a few has stalled solution of the three practical problems. Nonetheless, there is consensus that the practical problems exist.

Problem No. 1 is the combined sewer system that serves 60 per cent of Washington, including 35 per cent of its school system. During severe thunderstorms, rain water and raw sewage overload the Blue Plains Treatment Plant, which, with its finite capacity, acts as giant stopper. The balance is dumped, untreated, into the Potomac. The District's goal, therefore, is to eliminate the combined sewer system, or at least short-circuit it, and the Department of Environmental Services has enlisted an outside contractor to help do that.

Jean Levesque, the Blue Plains chief, and Brink of Air and Water Quality, know that replacing the combined sewer system would cost billions - "enough to make Metro child's play," said Brink.

For one thing, holding basins would have to be dug, but what size basins? Basins to accommodate the rainfall from a summer thunder squall? From Hurricane Agnes?

An unpredicted prolonged downpour would inundate Washington thoroughfares with raw sewage. Such a catastrophe was anticipated by Congress in 1917, but combined sewer construction proceeded nevertheless.

Practical problem No. 2 is abatement of non-point pollution. When heavy rains wash the suburbs and surrounding farmlands, the run-off finds its way into the Potomac. The brown broth contains pesticides and herbicides, dieldrin, chlordane, endrin, heptachlor, malathion, toxaphene and others not healthful for fish or man. Industrial wastes of high toxicity - mercury, arsenic and kepone - hide in the runoff.

How to control non-point pollution is the subject of a study undertaken by the regional Council of Governments. This so-called "Section 208 plan" is due next year, and its implementation cannot help but call for a few hundred million dollars more for Potomac pollution cleanup. Control of non-point pollution entails more than analyzing the effluent from a single pipe, issuing a permit and enforcing it. Non-point pollution control involves land use, local zoning, city and county governments, perhaps the restructuring of land beneath farms, parks and subdivisions already in existence.

Practical problem No. 3 is enlargement of the Blue Plains Sewage Treatment Plant. Here, too, money is paramount. In June, 1972, the cost of Blue Plains' ongoing modernization was supposed to be $500 million spread over the next five years. In December, 1974, the cost estimate had escalated to $1.4 billion spread over three years, and the escalator is still running.

Who should pay? The average Washingtonian has come to believe that Blue Plains is there to treat his sewage, but such is not the case. During 1976, 43.7 per cent of Blue Plains input came from the District; 49.6 per cent came from the Maryland suburbs and 6.7 per cent from nearby Virginia. Regardless of who pays, experts agree that when Blue Plains in fully operational (target date: October, 1979), its effluent will be sweeter than the water flowing alongside it.

Before Blue Plains can use its advanced treatment facilities, a towering problem must be solved. At present, Blue Plains generates 600 tons of sludge a day. That sludge is buried in trenches, trucked to landfill dumps, spread on area park grass or allowed to pile up. In October, 1979, Blue Plains will be generating 2,000 tons of sludge a day, and there's no guaranteed way to get rid of it.

The preliminary report of another outside contractor suggest that a final solution may lie in selling or giving the nutrient-rich sludge to farmers. What remained would be incinerated, with the eight planned incinerators consuming 45,000 gallons of oil per day, but with no means of recuperating energy contained in the sludge.

The ultimate question concerning the Potomac was posed this month by City Councilman Jerry A. Moore, chairman of the transportation and environmental affairs committee, who scheduled the June 29 hearing.

"How clean should the Potomac River be?" asks Moore. He answers rhetorically:

"How much are we willing to pay? With all the demands on the District's budget, we must set our priorities carefully. It may be nice to have a Potomac River or Anacostia River in which we can swim, but is it economically feasible?"

Mayor Washington has proposed revising the District's standards. A downward revision would please recreational interest, but it would worry area epidemiologists who, like Dr. Samuel Formal, an intestinal bacteriologist at Walter Reed, wonder why Washington has escaped major outbreaks of digestive tract diseases. The District's Department of Environmental Services, if its way be had, will lessen physicians' concern. Its position is that water quality standards should be increased in stringency. And the circle closes to money.

Next: how safe is the Potomac's fish catch, a major source of protein for poor people?