The thriving infant presidential candidacy of Walter F. Mondale is haunted by a ghost--the ghost of "President Muskie."

When Mondale enters the Democratic presidential race Monday, he will be in the strongest position of any non-incumbent contender since Edmund S. Muskie 12 years ago. A great deal of effort has gone into minimizing the chance that he winds up as thoroughly beaten as Muskie was.

Since Sen. Edward M. Kennedy (D-Mass.) pulled out of the race last November, polls have shown Mondale far in front of any other Democratic aspirant. He led the incumbent, President Reagan, by 12 points in the Gallup Poll last month.

He has the most experienced campaign staff and an unmatched network of alliances. They have been accumulating since his political apprenticeship with Hubert H. Humphrey, his role as Humphrey's 1968 campaign chairman, his 12 years in the U.S. Senate, his two campaigns for vice president, his four years of service in the Carter administration and his work as the busiest Democratic campaigner in the 1978 and 1982 mid-term elections.

He has Mississippi Gov. William F. Winter out front for him in the South and a warm friend in Massachusetts Gov. Michael S. Dukakis, top Democrat in Kennedy's home base. Former secretary of labor Ray Marshall is pushing his cause with organized labor.

Atlanta Mayor Andrew Young and Illinois Comptroller Roland Burris are expected to be early advocates with blacks. The hierarchy of the National Education Association is lauding him to teachers. His likely supporters in city halls range from Philadelphia's Mayor William Green to Seattle's Charles Royer.

But for all the healthy auguries, Mondale's managers still think about what happened to Muskie.

"The analogy is something we deal with almost on a daily basis," said James A. Johnson, Mondale's acting campaign chairman and longtime chief of staff who cut his political eye-teeth as a Muskie organizer.

In January, 1971, Muskie was the leading choice of Democrats for the nomination and was in a virtual dead-heat in opinion polls with President Nixon. But by the fourth primary of 1972, he was finished, for all practical purposes, and became a bystander in the battle in which George McGovern beat Humphrey for the nomination.

"I can cite a half-dozen reasons why the analogy doesn't hold," Johnson said the other day, mentioning that Mondale "is a more experienced national politician" and that the Democrats are "not a polarized party," as they were by the Vietnam war issue in 1972.

"But we can learn things from the Muskie example: You have to understand the rules of the nominating process, you can't assume that party leadership will deliver large numbers of voters, the candidate has to present a compelling case to the voters himself and, most of all, you can't take anything for granted."

Taking nothing for granted is the keynote of the organization Johnson heads. Its scope and experience provide the underpinning for Mondale's indelible winter-book standing as the front-runner.

Yet, as Muskie's case showed, and as Peter D. Hart, a Democratic pollster who has worked for Mondale in the past, remarked, "There is nothing harder than leading from wire to wire in this kind of race."

The burden of the front-runner is that he is expected to prevail everywhere, while an upset anywhere can undermine his whole structure of support. Should Sen. Alan Cranston, a superb fund-raiser with a rich home-state treasury to tap in California, surge ahead of Mondale in the next financial report, it will hurt. Should Sen. Gary Hart (Colo.) move into upset range by nonstop campaigning in Iowa or New Hampshire, it will hurt.

Should Sen. John Glenn (Ohio) look so strong in the polls that labor gets cold feet on endorsing Mondale, it will hurt. Should former Florida governor Reubin Askew, Sen. Ernest F. Hollings (S.C.) and Sen. Dale Bumpers (D-Ark.), a potential candidate, combine with Glenn to lock up the South against Mondale, it will hurt.

The front-runner has to be ready to compete everywhere with everyone--for conservative unionists with Glenn and militant feminists with Hart, for Vermont nuclear-freeze advocates with Cranston and Fort Worth defense contractors with Hollings. And he has to do all this knowing that the press and television will be watching for any slipups and probably magnify them in the telling.

So it is not surprising that no Boy Scout ever took more seriously than Jim Johnson or Mondale campaign manager Bob Beckel the injunction: "Be prepared."

"We've spent two years thinking through how the '84 race would develop," Johnson said, "and at every stage, we've tried to hit our target at the opening bell."

Through Mondale law partner and "senior adviser" John Reilly, the campaign monitored the work of the latest Democratic Party delegate selection commission more closely than any other candidate organization. Coincidentally or not, the new schedule, which allows almost no time for fund-raising or television blitzes for a candidate "discovered" by voters in Iowa or New Hampshire, appears to favor a front-runner and increase the odds against a late-blooming outsider.

Mondale was the first candidate to raise enough money this year to meet requirements for Treasury matching funds, doing so in a dazzling 48-hour tour de force. He has put out more than 400,000 pieces of mail in the last month in an effort to keep ahead of Cranston and other challengers in the dollar derby.

By year's end, he hopes to have raised at least $6 million and banked a substantial sum for the rush of contests coming next winter and spring.

Having scored well in the first two oratorical contest "cattle shows" in Philadelphia and Sacramento, he is targeted on two more in March, in Boston and Atlanta. There also is a straw vote at the Massachusetts Democratic convention April 9 and other showcases leading up to the October NEA and AFL-CIO endorsements, for both of which he is favored. If Mondale clears all of these hurdles without stumbling, he will have the inside track for the primaries.

But, as his managers concede, there also are developments that could complicate his plans or knock him off the track.

As a consensus candidate, seeking to keep a foot in every faction of the Democratic Party, Mondale is particularly vulnerable to a renewal of tribal tong wars, pitting one interest group or caucus against another.

He has moved nimbly to identify himself with every emerging issue, from protectionism to the nuclear freeze, preempting his rivals from finding the equivalent of the anti-Vietnam war movement, which McGovern used to dethrone Muskie.

Mondale has taken a calculated risk by intervening in Tuesday's Chicago mayoral primary on behalf of his ally, State's Attorney Richard M. Daley. His action drew criticism from black leaders supporting Rep. Harold Washington, and he faces political retaliation from Mayor Jane Byrne, if she wins renomination to a second term.

But for the most part, Mondale has so thoroughly avoided giving offense to anyone that some in his organization worry privately that he may be seen by the voters as no more than a walking compendium of every interest-group agenda in the Democratic spectrum.

"I'd like to see him say no to some people and talk about sacrifice for the common good," one senior adviser said.

Mondale also is trying to straddle the Mason-Dixon line. While his loyalty to Carter brings him some political dividends in Dixie, aides concede that he is viewed as "too liberal" to be the preferred candidate in some southern states, particularly in comparison with Glenn or the southern candidates.

But his organizers think these problems can be managed. "As we look at the Democratic Party," Johnson said, "we see less factionalism and more consensus than at any time since before the Vietnam war. While Mondale has to be clear and convincing on his substantive program, it is not necessary for him to make early decisions on issues that will alienate substantial segments of the party. It's not a question of moving left or right but of taking clear stands that will not split the party ideologically."

As for the South, Beckel, who ran the 1980 Texas campaign for Carter, insisted that "we are not conceding anything to anyone."

That is why Mondale will be campaigning in early March in the tiny town of Hawkinsville, Ga., and why his schedule for the remainder of the year will devote almost as much time to the early southern delegate-selection states of Florida, Georgia, Alabama, Mississippi and South Carolina as it does to Iowa and New Hampshire and Massachusetts.

The members of the Mondale high command sound like people who have thought of everything. It may be a false confidence. But if they prevail, it will be in part because they cannot forget "President Muskie."