The week started out well for Anthony Weiner, the Brooklyn-Queens congressman who seeks to sneak to the head of the Democratic pack of candidates for mayor.

Mr. Weiner managed to make his obligatory appearance at the Reverend Al Sharpton’s Martin Luther King Jr. Day festivities and kept his presence low key enough to spare him an excess of attention. Mr. Sharpton is a problem for candidates like Mr. Weiner, who seek to project a moderate image. Many feel that when the front-runner at this point four years ago, the then-city (and now state) Comptroller Alan Hevesi ended his long-time boycott of Mr. Sharpton and finally made an appearance at this event, his campaign began to slide.

There must have been jubilation in the Weiner camp the following day, when John Podhoretz declared in his New York Post column that “Weiner would be the most formidable general election challenger for Bloomberg. He’s smart, smooth, moderate and can hurt the mayor in Queens, Brooklyn, and Staten Island – where Bloomberg will need to do very well to offset the colossal Democratic advantage in the Bronx and Manhattan.” That such a glowing analysis appeared in a tabloid with a large outer-borough readership reinforced the perception that Mr. Weiner could reprise Ed Koch’s jump from Congress to Gracie Mansion that surprised the pundits back in 1977.

By the end of the week, Mr. Weiner’s joy turned to alarm when he was ensnared in an embarrassing campaign-finance flap. One of his supporters “bundled” 29 contributions made by money orders, a red flag to those who monitor the city’s increasingly Byzantine campaign finance laws.

The law rewards candidates with a $1,000 city check in “matching funds” if they collect $250 in contributions from a city resident. Those who contribute more, say $1,000, are matched only to the extent of the $250 maximum. But four $250 contributions yields a $4,000 match. So why not just break up your big contribution by running down to your local bank, check-casher, or even post office, and split your largesse into four equal money orders, using your name and those of three of your closest friends. This can work when your buddies are in on the scheme. But the temptation is enormous to keep going, even after you run out of “legitimate” partners.

That’s what happened to former Councilman Sheldon Leffler in his unsuccessful 2001 bid for Queens borough president. Mr. Leffler was sentenced to probation for returning a $10,000 contribution from a contributor, asking that it be broken into 40 individual contributions of $250 each. This turned the already generous $10,000 into a cool 50 grand, at taxpayer expense, unbeknownst to most of the 40 “donors.”

The matching-fund system has the potential for all sorts of mischief. Consider the 2003 re-election bid of Council Member Larry Seabrook, who represents the northeast Bronx. Despite the fact that he only faced a token Republican Party effort in the general election, Mr. Seabrook collected enough small contributions which, when matched with public funds, enabled him to pay a $35,000 fee to his brother Oliver to “manage” his “campaign.” Mr. Seabrook won with 88% of the vote in a race that no rational observer could suggest posed even a remote threat to him.

In Mr. Weiner’s case, since he acted quickly and returned the questionable funds, the story and attendant political damage will almost surely go away. Every major candidate has had similar problems.

Mr. Weiner’s chief Democratic rival, Fernando Ferrer, returned a $1,000 contribution in 1993 from a nonprofit group called Puerto Rican Home Attendants Services, Inc., which made the contribution to Mr. Ferrer and others out of city funds they received to provide services.

In 1997, Mr. Ferrer was criticized for accepting a $1,200 contribution from a private company, D.A.O.R. Security, that was implicated in the failure to protect women from sexual abuse at a battered women’s shelter and other locations servicing other facilities for the homeless. Again, Mr. Ferrer returned the funds.

Contributions to Mr. Ferrer from firms guilty of environmental infractions and with ties to organized crime, some of which were returned and others kept, was the subject of an extensive review of Mr. Ferrer’s fund-raising, which appeared in the March 4, 1997, edition of the Village Voice.

In the last mayoral campaign, Mr. Ferrer returned $7,000 to Joseph Pontoriero, who heads Connecticut-based Worth Construction. Worth had been “blacklisted” by the School Construction Authority for failing to answer charges that Mr. Pontoriero had ties to the Genovese crime family.

But none of this had any lasting effect on Mr. Ferrer, who is now the frontrunner. The lesson is to cut your losses early.

When Alan Hevesi allowed questions about the legality of his relationship with his consultant Hank Morris four years ago to fester for weeks, it left the perception of scandal in the public consciousness. This was one of the few instances that these questions about finance managed to stick and negatively affect a campaign.

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Mayor Bloomberg’s potential Republican opponents, investment banker Steven Shaw and former Council Member Thomas Ognibene, must be rubbing their hands with glee over the mayor’s fawning praise of Mr. Sharpton at the Reverend’s Martin Luther King Day event. The mayor likened Mr. Sharpton to Rosa Parks, the kind of remark that will not play well among the GOP rank and file.

Another Republican primary problem for the mayor is the unresolved labor contract with the police and firefighter unions. Particularly in Staten Island, there are few households that don’t have a cop or firefighter either in residence, or as a close relative or friend. The tragic loss of the three brave firefighters in two incidents on Sunday only underscores the political problem that the mayor might face if there is still no contract by September.