Washington — Appointment of a special prosecutor to investigate the affairs of Edwin Meese III may relieve some of the political pressure on the White House in this highly charged election season.
But it is not likely to defuse the general campaign issue of ''quality of governance,'' political observers say. Aside from the doubts about Mr. Meese, whom President Reagan has nominated to be attorney general, questions continue to emerge about actions taken by other Reagan administration officials.
This week, reports about Justice Department probes into the use of official limousines by Cabinet members' wives surfaced in the press. The White House said that Attorney General William French Smith, after one such probe, reimbursed the government about $11,000 for his wife's use of an official car since 1981. It also said presidential counsel Fred F. Fielding would look into the use of government cars by spouses.
After a request by White House counselor Meese, Attorney General Smith on Monday asked a three-judge federal panel to name an ''independent counsel'' to look into the many financial and other matters that were raised in the Senate Judiciary Committee hearings and that have cast a cloud over the Meese appointment. The special prosecutor is expected to have a mandate to look into the following broad issues:
* A number of instances of financial help that Meese received from individuals who later were given federal jobs. One case concerned an interest-free $15,000 loan given to his wife, Ursula, which Meese neglected to report on his financial disclosure statement. Meese termed this an ''inadvertent'' omission.
* Meese's promotion in the Army Reserves. The Army inspector-general's office found that Meese had been improperly transferred from retired to active-reserve status and then promoted to colonel. Meese last month asked to return to retired status.
* The ''debategate'' papers. Meese said repeatedly in the hearings that he did not recall seeing numerous documents forwarded to him concerning Carter campaign information.
Meese has named three lawyers to help in his presentation to a special prosecutor: E. Robert Wallach, a San Francisco trial attorney and close friend; Leonard Garment, who represented Richard Nixon during the Watergate investigation; and Max M. Kampelman, who recently served as head of the US delegation to the Conference on Security and Cooperation in Europe.
The White House, meanwhile, is considering the appointment of an interim attorney general so that Mr. Smith can return to his law practice in California and help with the election campaign.
Whether the President can politically survive the Meese ''time bomb'' is a moot question. Some political analysts believe Reagan will continue to be hurt unless he asks Meese to step aside. Even if the special prosecutor eventually issues a report vindicating Meese of any criminal wrongdoing, the appearance of insensitivity to ethical standards could remain to tarnish the administration.
''From the standpoint of the White House,'' says John Sears, a former GOP political strategist, ''if there's a prolonged process with a special prosector that could bring you close to the election, at that point you have to ask whether you want to go with (the appointment).''
''The longer this drags out, the worse it will be,'' says presidential expert Thomas Cronin of Colorado College. ''Depoliticizing the job of attorney general by appointing someone of quality - like William Webster - would be a shrewd political step right now. No president, Republican or Democratic, can have an attorney general who does not look absolutely above board.''
''Unless he does something comparable to the removal of James Watt,'' says Princeton scholar Fred Greenstein, ''Reagan is politically going to be exposed by the Democrats to the whole questionof favoritism and scandal. This will also cause brushfires in the Republican Party - similar to the '58 election when Eisenhower tried to stand by Sherman Adams but had to get rid of him.''
Reagan campaign stategists say that, assuming no wrongdoing is found by a special prosecutor, the President will keep Meese's name in and that the Senate will confirm him. ''If the only thing found is an 'oversight' in listing a loan, '' says one top operative, ''the American people will not hold that against him.
No one who really knows Meese thinks he was trading jobs for financial favors.'' Some of those who helped Meese had to be begged to come to Washington, said the operative.
On Capitol Hill some Republicans speculate that Reagan may have skillfully neutralized the Meese affair. They reason that the appointment of a special prosecutor in itself shows that the White House is ''doing the right thing.'' Also, an investigation will take at least three or four months, by which time Congress may have recessed until after November. The Senate Judiciary Committee, then, would not act until next year. But the general consensus seems to be that this is a politically sensitive issue that won't go away.
''It's not just a matter of Meese as attorney general,'' comments Stephen Wayne, another presidential scholar, ''but the general pattern that wealthy people are taking advantage of their positions. It reinforces that there are two standards of ethics.''
With the economy doing well, adds Dr. Wayne, the Democrats will be eager to keep the ethics issue alive.