When a museum discovers that one of its major exhibits has significant inaccuries and shortcomings, what should it do? The answer seems obvious: Take corrective action, and as soon as possible.

Yet in the case of the Smithsonian Institution, the obvious is not so obvious at all. Since early last year, the Smithsonian's Museum of History and Technology has known that its sharecroppers' house, on exhibit in the second floor Hall of Everyday Life, is a gross distortion of what the four-room, one-and-a-half story dwelling was like when it sheltered a succession of tenant families on the Mulliken-Spragins' farm in Mitchelville, Prince George's County (now the site of Bowie's Pointer Ridge Shopping Center).

The problems were catalogued in an April 1978 report to the Smithsonian by a consultant, historian George W. McDaniel, who had been hired by the museum to trace the families who had lived in the house and to provide a reinterpretation of the entire setting, inside and out.

Finding members of the 11 black families who had lived in the house between 1896 and 1967 turned out to be an incredibly successful undertaking, and through their often vivid recollections, McDaniel was able to breathe some flesh and blood into the history of this humble house.

But the house itself was another matter. Through his research, McDaniel found that it was being exhibited with its back as its front. The depth of the interior was shortened, cramping rooms and making it difficult to furnish them. The larger front room was the kitchen, not a sitting room, as portrayed.

As exhibited, the interior is almost devoid of paint. The drab look is not the result of neglect by the house's occupants but exposure to the elements after the time the place was abandoned in 1967. In life, the walls were first whitewashed and then painted -- a light green, according to Vivian Hartley, whose husband, Edward, grew up in the house.

But more than drabness, there is a lifelessness about the house -- and this perhaps is the greatest injustice that has been done in the Smithsonian's re-creation. The few furnishings and artifacts have a contrived look about them.

There is little to suggest what Dr. McDaniel wrote in his report:

"Because there were families in this house, a wide range of household activities went on. As families, they cooked food, ate meals, washed dishes, bathed, sewed clothes, took medicine, played music, churned butter, swept floors, rested and relaxed, washed clothes and selpt . . .

"Outside the house, clothes were washed and dried, water gathered from the spring, stove wood chopped and stacked, chickens fed and housed, and a path worn to the outside toilet . . ."

McDaniel wanted to suggest at least some of these activities, and his entire reinterpretation, including a new and expanded explanatory legend, would probably cost, he estimates, $10,000 to $15,000 -- not, you would think, an inordinate sum to correct some major distortions, in a exhibit in a major museum.

Dr. McDaniels says: "I think it's commendable that the Smithsonian has chosen to exhibit the sharecroppers' house. But I do believe the house should be made an accurate portrayal of the way of life of sharecroppers, since theirs is the heritage of millions of Americans, both black and white.

Rodris Roth, the curator in the Division of Domestic Life, who was in charge of the exhibit, acknowledges, "Knowing what we know now, the house is not as accurate as it could be." But, she says: "We aren't proposing any changes now . . . There are other priorities. This is not a high priority."

It is ironic that the long-victimized Southern sharecropper should still come out on the short end, even when one of his putative advocates, in the form of the Smithsonian, steps forward.