The Washington Post incorrectly reported Monday that the United Mine Workers Union is backing Sen. Edward M. Kennedy (D-Mass.) for president. The UMW has not officially endorsed a candidate.

Despite publicity generated by a sprinkling of union endorsements of Democratic hopefuls, most of organized labor is sticking to the center lane in the heavy traffic generated by the 1980 Democratic presidential race.

"There is no real, solid indication of movement either way," said Saul Miller, chief spokesman for the AFL-CIO. "There is a feeling among many people in the labor movement that this is not quite the point at which to commit themselves."

The candidates strenuously seek support from labor unions, despite indications that union chieftains today cannot always deliver the votes of their members the way they once did.

So far, President Carter has won either personal or organizational endorsements from at least seven major unions or their leaders, including the 1.3 million-member National Education Association (NEA).

Carter's top challenger, Sen. Edward M. Kennedy (D-Mass.), has picked up similar support from at least eight major unions or their leaders.

California Gov. Edmund G. (Jerry) Brown Jr. is last in the Democratic race for the union vote, with only one major organization, the Service Employes International Union, offering him its backing.

No major union official has endorsed a Republican candidate -- a circumstance that is likely to remain unchanged, labor leaders say.

There was some speculation that organized labor, which has been feuding with Carter almost since he took office in 1976, would move quickly toward Kennedy after the Massachusetts senator declared his candidacy Nov. 7.

It has not happened.

"It's hard to pull people from the middle," said William W. Winpisinger, president of the International Association of Machinists (IAM), one of the first unions to back Kennedy publicly.

"Too many people are playing it safe," he said.

Part of the reason for the apparent lack of commitment is that many union leaders do not see much difference between Kennedy and Carter, and are reluctant to choose sides in a batle they feel could cripple the Democratic Party and yield a Republican victory.

Even here in Ann Arbor, where hundreds of liberal and avowedly socialist labor leaders gathered to discuss labor's future in the 1980s, there was ambivalence, and sometimes downrights hostility, towards choosing one Democratic candidate over the other.

That was made clear to Winpisinger Friday night when he called upon the labor conference delegates to "bring down the government" of Jimmy Carter and put Kennedy in the White House. He was roundly booed. One delegate shouted from the audience that "there's not a dime's worth of difference between a Kennedy and a Carter."

The AFL-CIO, which has 105 affiliates representing 13.6 million of the nation's 20 million unionized employes, will defer any presidential endorsement until after the party nominating conventions.

In this void, both the Carter and Kennedy camps are claiming to have the allegience of the nation's organized workers.

Besides the NEA, which is grateful to Carter for backing the new Department of Education, the president has support, in the form of personal or organization endorsements, from the Amalgamated Clothing and Textile Workers, the Seafarers International Union of Northern America, the International Ladies Garment Workers Union, the Communications Workers of America, the United Food and Commercial Workers Union and the International Union of Operating Engineers.

Kennedy, despite the reaction here to Winposinger's call for liberal unity behind his candidacy, does seem to be getting much of his support from the liberal, more activist wing of the labor movement.

Besides the machinists, whose president is regarded as being the most liberal of the nation's labor leaders, Kennedy has won either individual or organizational endorsements from the Bricklayers, the International Chemical Workers Union, the Painters, the United Mine Workers, the United Rubber Workers, the International Union of Electrical Workers, and the United Auto Workers.

Kennedy also is espected to win the support of Albert Shanker, president of the NEA's rival, the American Federation of Teachers (AFL-CIO).

In several cases, Carter and Kennedy share support from the same groups. For example, the president of the Brotherhood of Railway and Airline Clerks, Fred Kroll, has endorsed Kennedy. The union's vice president, Jack Otero, has endorsed Carter.

Both Kennedy and Carter claim substantial backing from the AFL-CIO's fastest-growing affiliate, the million-member American Federation of State, County and Municipal Employes. But AFSCME has not officially endorsed either.

And despite UAW President Franser's endorsement of Kennedy last week, Carter promoters claim with some justification to have good-to-strong support among the nation's 1.4 million unionized auto workers.