American taxpayers have saved themselves $12.5 million by their unprecedented cooperation with the 1980 census. The latest once-a-decade headcount may go down as the most successful in the nation's history.

Census Bureau officials say they have encountered a variety of unforeseen snafus -- some comic, some tragic. And, as usual, it has been difficult to obtain an accurate count in city slums.

But overall, federal officials say, the April 1 census has been a "phenenomenal" success.

The Census Bureau says that almost 86 percent of the forms recieved at occupied residences in late March have been sent back to district offices -- a return rate exceeding even the most optimistic projections.

The census budget of $1 billion was based on an expected rate of 80 percent.

So, officials estimate, $12.5 million has saved in expenses of tracking down people who were not expected to return their forms but who did.

"Apparently, a lot of people thought, 'Hey, it does make a difference,' instead of, 'What the hell, the government is gettin nosy again.'" said Rex Pullin, associates director of the Census Bureau. "I'd have to say that this year's census will be remembered as the most successful ever undertaken in this country."

The real test, according to Pullin, will come in mid-June when mayors have a chance to challenge the government figures for their cities and towns.

"We'll judge our success on whether local officials agree or disagree" with the federal population and housing counts, he said.

About $50 billion dollars in annual revenue-sharing funds and other federal grants will be allocated based on the new census count.

Before the first head was tallied, Detroit filed suit challenging the expected undercounting of blacks in that city. And mayors of Atlanta and Phoenix complained to Congress that the 10-day period in which local governments was too short to double-check the reams of statistics.

The Census Bureau acknowledged that its 1970 count failed to tally 7.7 percent of black and 1.9 percent of whites. Ten years ago, 1,900 complaints were filed by mayors claiming undercounts.

"There are some mayors who are going to complain no matter what the figures show," Pullin said.

Several unforeseen problems cropped up during the census:

Afire in the Framingham, Mass., district office destroyed 100,000 completed forms.

Overzealous postal workers in Lincoln, Neb., "wrote their own procedures" and delivered forms to the wrong houses, which caused census officials "some moments and headaches."

The rioting in Miami forced the shutdown of two census offices, and the National Guard was summoned to erect barbed-wire barriers and a protect completed forms at rifle point.

The eruption of St. Helens forced the shutdown of four census offices in Washington State, but there was not damage to forms.

A 5,000-square-foot section of roof at a census processing site in New Orleans collapsed under heavy rains, nearly destroying expensive electronic gear.

The official deadline for completion of all work is Dec. 31. State-by-state population counts must be on President Carter's desk by Jan. 1 for purposes of assigning seats in the House.

Fourteen of the 435 House seats will change states, with Sun Belt areas in the South and West gaining more members in the house.