Washington — Two broad developments now cast uncertainty about the nomination of Edwin Meese III to be attorney general of the United States. They also threaten to make the presidential nomination a factor in the election campaign:
* The Justice Department has begun a preliminary investigation of the White House counselor's financial transactions. Under the 1978 Ethics in Government Act, it must decide whether there are sufficient grounds to warrant appointment of a special prosecutor.
* US District Court Judge Harold H. Greene is expected to decide soon whether to order the Justice Department to request a special prosecutor to investigate how Reagan 1980 campaign aides, including Edwin Meese, obtained documents from the Carter reelection campaign. In connection with a suit brought by a law professor at George Washington University, Judge Greene has already criticized US Attorney General William French Smith for his department's limited investigation of the matter.
Even after the Senate Judiciary Committee this week postponed hearings on the Meese nomination pending the FBI investigation, President Reagan reaffirmed his support for his close friend and confidant. But White House aides are known to be concerned about the adverse political implications of the Meese affair if the Democrats begin hammering at it as a campaign issue.
Asked about the ''sleaze factor'' in the campaign, Sen. George McGovern told reporters Tuesday that he expected to see more mention of it. He added that candidate Gary Hart might be able to exploit it to his advantage since, unlike Walter Mondale, he had no connection with the Carter presidency and the political problems it encountered over Bert Lance, who resigned as budget director following a Senate inquiry into his banking practices.
Earlier this year, before he surged ahead in the Democratic contest, Senator Hart accused the Reagan administration of a record of unethical conduct. He charged that about 50 high-ranking officials had faced serious allegations of criminal wrongdoing, including Meese, CIA director William Casey, USIA director Charles Wick, and Attorney General Smith. He also said that at least 25 Reagan appointees had resigned, been fired, or had their nominations withdrawn in the wake of scandal.
Republican as well as Democratic lawmakers are raising doubts about the Meese appointment. Sen. Charles McC. Mathias Jr. (R) of Maryland has suggested that Mr. Reagan take account of the ''political fallout'' of the controversy and that an attorney general must be ''perceived to be above suspicion.'' Sen. Charles E. Grassley (R) of Iowa has said he may not vote for Meese following the latest disclosure of Meese's failure to report a $15,000 interest-free loan to his wife. Senate minority leader Robert C. Byrd (D) of West Virginia has stated flatly he would not vote for confirmation.
Civic organizations also are focusing on the issue. In a letter to all members of the Senate, Common Cause chairman Archibald Cox on Tuesday urged the Senate to turn down confirmation of Meese. Noting that Common Cause had never opposed a Cabinet-level nomination, the former Watergate prosecutor stated:
''The record (before the Senate Judiciary Committee), even when read most favorably to Mr. Meese, shows an extraordinary insensitivity to - even disregard for - the ethical mandates that public office should not be used nor even appear to be used for private advantage, and that appointment to public office should never be distributed in return for private favors.''
Ostensibly the FBI investigation will look into the $15,000 loan to Meese's wife, Ursula, from a friend, Edwin Thomas. Mr. Thomas and his wife, Gretchen, later received well-paying federal jobs. Meese has apologized to the Senate committee for ''inadvertently'' neglecting to disclose the loan, as well as the stock bought with the money, on his annual financial statement. The financial statement has now been revised.
Beyond that loan, however, are several other instances where Meese received financial help from friends who later obtained appointments to federal posts. The Justice Department may also investigate these cases.
The White House counselor denies that these appointments were linked with the financial aid. But what troubles legislators is an apparent pattern in which those who helped Meese ended up with federal jobs. A further subject of concern is Meese's promotion in the Army Reserve.
Little attention had been paid in the Congress to ''debategate'' pending issuance of a report on investigation of the matter by a House subcommittee. The report is due out in a few weeks and will include the results of the investigation by the Justice Department, which so far has released only a summary of its inquiry.
With release of some of the subcommittee documents to the Senate judiciary panel, however, interest has been aroused about Meese's knowledge of how the Reagan 1980 campaign may have used briefing materials prepared for President Carter for a presidential debate. During strong questioning at his confirmation hearing, Meese repeatedly said that to his recollection, he had no knowledge of or took no part in actions involving Carter materials.
Although this issue could be embarrassing to other White House aides as well, political experts doubt that the latter would put pressure on Meese to remove his name from consideration. ''Meese's too close a friend of the President, and such pressure could backfire,'' says Norman Ornstein of the American Enterprise Institute. ''It may occur to Meese, without any pressure, that he's become too much of a liability. But I doubt he would do anything until he was convinced that he was dead.''