As the broiling sun shimmers off its gleaming white superstructure, the 710-foot Potomac Trader eases into Brazos Harbor and three tugs nudge the tanker, laden with 280,000 barrels of Mexico's best crude oil, into a berth alongside the Seaway Terminal.

This shipment of Mexican Isthmus crude, when put through a modern refinery, will yield 6 million gallons of gasoline--enough to keep all the cars in Washington area running for two days--along with an additional 5 million gallons of home heating oil and petroleum products.

But the $8 million cargo being unloaded from the Potomac Trader will not find its way to America's gas pumps soon. Before the week is out, the 280,000 barrels of crude pumped out of the ground in Mexico will be injected back into the earth here in Texas.

The Potomac Trader's oil is destined for storage in the U.S. Strategic Petroleum Reserve--an increasingly controversial $14.5 billion effort to turn the alligator-infested bayous and wetlands along the coast of Louisiana and Texas into a surrogate Arab oil state.

Night and day, throbbing pumps suck millions of gallons of fresh water out of the Brazos River and the Intra-Coastal Waterway and force it down 2,500-foot-deep wells to dissolve the rock-like center of huge salt domes.

The salty brine then is flushed from the bowels of the earth, leaving giant underground caverns--almost half again the size of New York's World Trade Center--that are being filled with oil at a current rate of about 250,000 barrels a day. There are 42 gallons to a barrel.

More than 330 million barrels of crude now are stored in America's new man-made oil fields--a stockpile equal to more than a year of the total production of a major oil nation such as Kuwait.

This huge reservoir of crude temporarily could be used to augment America's domestic petroleum supply in the event of a world crisis, and ease the kind of gasoline panic that erupted when Iran tumbled into turmoil and cut off oil exports in 1979.

But the Strategic Petroleum Reserve, launched with a patriotic fervor that made storing "oil in the ground" a higher priority than worrying about the cost, is coming under increasing attack for mismanagement, fraud and waste.

The reserve also has become the focus of a growing national policy debate over whether the government should be filling it more rapidly at a time oil prices are relatively low, or whether enough billions already have been poured into the ground.

With net American oil imports currently running about 3.9 million barrels a day, the reserve now contains enough crude to take up the slack in the unlikely event that all foreign oil shipments to this country were cut off for almost three months.

The official Reagan administration plan is to continue leaching out salt caverns and filling them with crude until a stockpile of 750 million barrels has been achieved, which will take at least an additional $18 billion and seven years.

But with the administration already trying to defer oil purchases to save money, many observers expect enthusiasm to wane when the stockpile reaches 500 million barrels--a target that may be reached as early as 1985.

The question of how large the reserve should be, however, is only one of the fundamental issues being raised by Congress. Others include:

* What type of emergency should trigger use of the reserve?

* Does the administration have an adequate plan for distributing oil from the reserve in a crisis?

* Could the government actually get the oil out of the ground in timely fashion?

* Is the reserve, which most likely would be used at a time of turmoil in the Arab oil states, vulnerable to sabotage?

These concerns--and a mounting belief on Capitol Hill that the Energy Department has been lax in addressing some of them--led Energy Secretary Donald P. Hodel to shake up the management of the reserve last month.

Hodel took the action after Rep. Mike Synar (D-Okla.), who has emerged as a leading House expert on the reserve, became the first lawmaker to visit any of the storage sites. At subsequent hearings, Synar pronounced himself uncertain "whether to laugh or cry" about inept management.

"The reserve is of great strategic importance to this country," Synar said. "It also is one of the largest and most expensive procurement projects undertaken by the federal government. Since the project is almost half complete, it is essential that we not allow the mistakes of the past to recur in the future."

Many of the problems that have bedeviled the reserve arise because, when construction was launched in a crisis atmosphere six years ago, few key players had any real idea what was involved in managing such a complex undertaking.

Even though four of the storage sites are in Louisiana and one at Bryan Mound just three miles from the Seaway Terminal here, the government did not even set up a management office outside Washington to oversee the program until a year after the first oil was put in the ground.

The result was chaos, with contractors working on various pieces of the project literally tripping over each other in a sea of mud, accidentally uprooting and destroying instruments and cables. With security at the sites next to nonexistent, valuable equipment simply walked away.

The contractor installing automated central control systems at three of the storage sites also walked away in frustration and disgust, leaving behind inoperable systems that the Energy Department accepted on an "as is" basis.

At the West Hackberry dome in Louisiana, lax safety and operating procedures also resulted in a major fire and oil spill that claimed the life of a worker in 1978.

But a recent visit to two of the storage sites--Bayou Choctaw near Baton Rouge in Louisiana and Bryan Mound here--indicates the situation is improving, albeit not perfect.

The automated systems, designed to permit operation of valves and pumps from a control panel, finally are being completed.

Contractors are installing "Israeli-type" security fences around dirt clearings called "well pads" that have been elevated to slightly above swamp level as a defense against flooding. These unobtrusive pads are the only above-ground indication that a cavern with 10 million barrels of crude lies immediately below.

The procedures followed in unloading the Potomac Trader, one of 15 tankers arriving here each month with oil for Bryan Mound, also suggest that the government is anxious to avoid any recurrence of charges that the Strategic Petroleum Reserve has not always obtained the quantity and quality it paid for.

Winches still were securing the Potomac Trader to the dock when Severo Pena of the Defense Contract Audit Agency and Kathi Sheeley, representing a private firm under contract to the Energy Department, began making their way across the dock to collect samples of crude from the tanker for tests.

"We are responsible for quality and quantity," Pena said, perspiration soaking his brow. "We're going to board the ship, gauge each tank, and we're going to calculate the barrels in each tank. Then we're going to take a sample from each hatch."

Quality tests are quickly run on the samples, and the measurements of oil in the ship's tanks are compared to the ship's manifest. Pena said that on one occasion an inspector found "10,000 barrels of water in the tanks that weren't there when the ship was loaded."

Since that particular case involved a supertanker, the 10,000-barrel discrepancy represented an error margin of less than 1/2 of 1 percent, Pena said. But with the world price of crude oil running $28.70 per barrel, the water would have cost U.S. taxpayers more than a quarter of a million dollars.

"But the last ship," Pena said, "we were within 100 barrels. We don't always get that close because of differences in pressure and temperature. But if there is more than 1/2 of 1 percent difference, we investigate."

In addition, the oil will be measured again as it is pumped off the Potomac Trader and routed through a Seaway Terminal meter; after it is moved three miles by pipeline to Bryan Mound, the crude will be metered one more time as it flows into above-ground holding tanks.

"I can't think of any better way to protect the government unless we had somebody riding herd with a shotgun, like on the old stagecoaches," said James Harkins, assistant manager for operations. "Industry doesn't go to these extremes. But with the price of oil the way it is, it has to be done."

From the holding tanks, the crude will be routed through other pipes to one of the 12 new salt caverns still being leached out on the 500-acre site here.

As the oil is injected into the earth, it collects in the upper part of the cavern, and it, too, forces brine from the cavity. The brine is piped 12 miles out into the Gulf of Mexico, where it is dispersed.

In the event of an oil crisis, the crude would be withdrawn from the caverns by reversing the process. "You'd take precisely the same equipment and pump in fresh water," said C. Curtis Johnson, manager of the reserve, "and oil would come out instead of brine."

Several experts have contended that because of the age of the pumping equipment, the harsh use it has been subjected to and the growing problem of obtaining spare parts, it might be difficult to withdraw oil over any extended period at the planned 3.5 million barrels a day.

Reserve officials, however, are infuriated at the suggestion.

"The thing that concerns me is that people keep asking, 'Gosh, can we get it out of the ground?' " said Johnson. "The answer is yeah. Not only yeah. Hell yeah!"