Washington — On the face of it, the indictment of Labor Secretary Raymond J. Donovan might be expected to cause serious political problems for President Reagan. But political observers say the Democrats may have a difficult time making it a decisive issue in the campaign. They cite these reasons:
* Mr. Reagan has demonstrated an extraordinary capacity for distancing himself from the misdeeds or alleged crimes of members of his administration. Even when media attention was focused on such figures as White House counselor Edwin Meese III, recently absolved of any criminal wrongdoing in matters of personal financial dealings, the President's approval ratings did not drop in the opinion polls.
* Republicans can make the case that the indictment is politically motivated, coming as it does just before the first presidential debate and within just one month of the Nov. 6 election. Many voters may see it as an element of political mudslinging.
* The alleged crimes charged against Mr. Donovan (who pleaded innocent at his arraignment Oct. 2) concern a period before he took office and do not involve administration policy. This is not therefore a Watergate type of development. Also, Donovan is not a well-known figure among the electorate.
* Walter Mondale's mild reaction to the Donovan indictment indicates the Democrats either don't see much political gain there - or worry the issue could backfire.
''I presume innocence,'' Mr. Mondale said as he left Washington Tuesday for a campaign trip. ''I think what really counts now is how the President handles this matter.'' Mondale suggested that Mr. Reagan should find out if there are ''reasonable grounds'' for the charges. If so, said Mondale, only then should Donovan be removed from office. Democratic insiders urged the candidate to make the Donovan situation a major issue at the debate coming up this weekend.
''At this stage of the campaign, the indictment can only have a minimal effect,'' says Austin Ranney of the American Enterprise Institute. ''Most people have made up their minds about Reagan and all the evidence is that he is detached, in the public mind, from the rest of the administration.''
As Donovan presented himself for arraignment in New York, a question stirring here was: Why did a Bronx grand jury indict the labor secretary after a federal special prosecutor independent counsel had apparently cleared him?
On June 28, 1982, special prosecutor Leon Silverman announced he had found ''insufficient credible evidence'' that Donovan had been present at an illegal payoff to a union official, or that he had ties to organized crime. A grand jury , which had been called, agreed. But in his final report Mr. Silverman did say there were a ''disturbing'' number of allegations of Donovan wrongdoing.
The Bronx grand jury's charges center on one of the allegations - that Donovan's firm, Schiavone Construction of Secaucus, N.J., along with a subcontractor, had extracted billions of dollars from New York State through phony billings.
Silverman did investigate this charge, and decided it could not be proved. A Senate staff member says the Department of Justice has refused to turn over files dealing with Schiavone and the subcontractor, Jopel's Construction & Trucking Company Inc., of Bronx, N.Y., because the investigation is still ''active.''
Silverman, in a telephone interview earlier this year, said that he had conducted a thorough investigation and that no one had told him he should ''do anything more.'' He could not be reached for comment on Monday's action by the Bronx grand jury.
The Ethics in Government Act of 1978 established procedures for appointing special prosecutors to investigate possible lawbreaking among high government officials. Since the law was passed, four prosecutors have been named, but no indictments have resulted.
Nonetheless, the Donovan indictment and arraignment confront the Reagan campaign with the delicate problem of damage control. The strategy, in effect, is to button up the problem. Reagan-Bush campaign officials refuse to talk about the possible political fallout, suggesting that they are trying to keep the President insulated from the whole affair.
The news about Donovan broke Monday afternoon as the President was campaigning in Mississippi, and he immediately granted his labor secretary's request for a leave of absence without pay. The White House said Reagan had not spoken directly with Donovan and had ''no specific reaction because the matter is in the courts.''
According to press reports, some of the President's political advisers wanted Donovan to resign. But Reagan has built a reputation of strong loyalty to his aides, an attribute thought to be appealing to many Americans.
''There's no evidence or reason to believe this will be seriously damaging,'' says David Gergen, a former White House aide. ''They have to wait and see how it sorts itself out. It's an indictment, not a determination of guilt.''
But the indictment does raise anew the issue of ethics in government. And it could add to a perception among many that the Reagan administration is vulnerable on ethical considerations.
Rita Lavelle, assistant administrator of the Environmental Protection Agency, was, for instance, convicted of perjury and of obstructing a probe of the EPA.
Deputy Defense Secretary W. Paul Thayer resigned in order to defend himself in an insider-trading suit filed by the Securities and Exchange Commission.
National-security adviser Richard Allen resigned after $1,000 and three watches were discovered in his White House office safe.
Mr. Meese, who was nominated to be attorney general, was cleared of any criminal conduct by an independent counsel. The investigation went into Meese's possible role in helping obtain federal jobs for people who helped him financially. But it did not take up alleged improprieties or poor ethical judgment involved in his financial dealings.
There was a time when the so-called ''sleaze factor'' looked like a hot issue for Democrats. Democrats, however, have struggled with their own problems since then.
First, there was the embarrassment of the Bert Lance appointment - quickly reversed - as a top official in the Mondale campaign. The appointment reminded voters of Mr. Lance's own indictment (he was later cleared of some charges; others were dropped) during the Carter administration. Then came Geraldine A. Ferraro's woes - a whole list of problems, including questions about the accuracy of her personal financial reports to the Congress. She is now under investigation by the House Ethics Committee.
A campaign aide, asked why Mondale isn't hitting the Donovan indictment harder, said the candidate prefers ''not to get into any personal attacks.''
''The Democrats can try to use the Donovan indictment as an illustration that this administration is rife with wrongdoing,'' says political scientist William Schneider. ''It confirms an image that Reagan associates with a lot of rich wheeler-dealers. But this has not really worked, partly because of Reagan's personality and partly because people believe he is a loyal, trusting president.''