The Democratic candidates running for mayor of New York City differ on many issues, but they tend to agree on one thing: All aspire to be different from Mayor Bill de Blasio, a Democrat in his second term whose approval rating dropped after his failed run for president last year.

On Friday, the city Department of Investigation released a report that sharply criticized the de Blasio administration for its handling of the Black Lives Matter protests earlier this year.

The findings were uniformly welcomed by the mayoral hopefuls, many of whom have been critical of the police tactics deployed. One went further, vowing to remove the police commissioner, Dermot F. Shea, if elected mayor.

One other way they vow to differ from Mr. de Blasio? They say they will ride the subway more often.

Here’s what you need to know about the week that was in the mayor’s race:

Who’s landing the big political guns for hire?

The huge field of candidates running for mayor — as well as the City Council and other local races in New York — is expected to be a bonanza for campaign consultants, and some key hired guns have landed in some interesting places.

L. Joy Williams, the president of the Brooklyn N.A.A.C.P., signed on with Raymond J. McGuire, a Black businessman. She was an adviser for Cynthia M. Nixon, the actress and activist who ran for governor in 2018.

Ms. Williams could help Mr. McGuire, a first-time candidate, reach Black voters in Brooklyn, especially women — a critical constituency that will be courted by other Black candidates, including Eric Adams, the Brooklyn borough president, and Maya Wiley, a former top counsel to Mr. de Blasio and MSNBC analyst.

Scott M. Stringer, the city comptroller, hired Rebecca Katz, a confidante of Mr. de Blasio’s who helped shape his image, but has been critical of the mayor recently. Ms. Katz has worked for progressive candidates, including Representative Jamaal Bowman.

Ms. Wiley hired Alison Hirsh, who left Mr. de Blasio’s administration earlier this year and worked for the powerful 32BJ local of the Service Employees International Union; and Maya Rupert, who worked on the presidential campaigns of Julián Castro and Elizabeth Warren.

Mr. Adams hired Katie Moore, political director of the influential Hotel Trades Council.

But the competition is fierce.

Abbey Lee Cook, the campaign manager for Representative Max Rose, who just announced his mayoral bid, already signed up to work with Tali Farhadian Weinstein, a former prosecutor who is running for Manhattan district attorney. A high-profile political firm led by Stu Loeser, an aide to former Mayor Michael R. Bloomberg, is also working on Ms. Weinstein’s campaign.

Be like Bill de Blasio and ride an SUV? Not likely.

Mr. de Blasio has been criticized for not riding the subway regularly to see riders’ commuting misery up close, opting instead to view the city from the windows of his chauffeured SUV.

Admitting that he could do better, Mr. de Blasio told reporters last week that he would ride the subway soon, to show New Yorkers that it is safe during the pandemic.

But some candidates are pledging to do more. Shaun Donovan, a former housing secretary under President Barack Obama, promised to ride the subway every day. Mr. McGuire said in an interview that the subway is the “easiest, cheapest and quickest way to get around,” and that he would ride the subway as much as possible if elected.

Others followed suit after Streetsblog, a website dedicated to street safety, inquired about their commuting habits. Mr. Adams said that he was already a regular subway rider, and would continue to be one if elected mayor.

Carlos Menchaca, a Brooklyn city councilman, committed to taking the subway or riding his bike while “significantly limiting car trips.”

It should be noted that Gov. Andrew M. Cuomo actually controls the subway, and is rarely seen aboard a passenger train. But the mayor appoints members to the board of the Metropolitan Transportation Authority, the agency that oversees the subway, and can use his or her bully pulpit to help the system, which is in a deep financial crisis.

Being early contenders pays off for Stringer and Adams

The city’s Campaign Finance Board announced last week that it had approved more than $17 million in matching-funds payments to 61 candidates in races across the city next year.

The initial outlay underscored the advantages of establishing early candidacies: Mr. Adams’s campaign qualified for about $4.4 million in matching funds, while Mr. Stringer’s campaign received about $3.3 million.

No other candidate met the dual threshold of raising at least $250,000 in contributions of $250 or less from at least 1,000 city residents by July.

Mr. McGuire is not participating in the 8-to-1 matching-funds program, which effectively turns a $10 campaign contribution from a city resident into $90. Lupé Todd-Medina, a spokeswoman for Mr. McGuire, said the campaign felt good about not accepting taxpayer resources during a financial crisis and could raise enough money to get its message out.

But Paul J. Massey Jr., a wealthy real estate executive who ran against Mr. de Blasio in 2017, suggested that mayoral candidates like Mr. McGuire may regret not participating in the matching-funds program. He said his biggest mistake as a first-time candidate was deciding to opt out; Mr. Massey raised $1.6 million, but spent it quickly on consultants and lent his campaign $1.2 million.

“Being involved in the matching-funds program or writing checks the size Michael Bloomberg wrote are probably the few practical paths to financing a campaign for mayor,” he said in an interview.

A ‘monumental failure of leadership’

One candidate called for an elected Civilian Complaint Review Board and “massive disinvestments” in the New York Police Department. Another said the mayor demonstrated a “monumental failure of leadership.” And one candidate called for the dismissal of the police commissioner.

The reactions came in response to a Department of Investigation report that concluded that the Police Department’s use of aggressive tactics had inflamed the summertime protests over the death of George Floyd, and violated protesters’ rights.

The strongest reaction came from Dianne Morales, considered among the most progressive candidates in the race, and Ms. Wiley, a former chairwoman of the Civilian Complaint Review Board, which investigates accusations of police misconduct.

Ms. Morales said the Police Department committed “acts of violence,” and called for “dedicated prosecutors” for police misconduct.

Ms. Wiley said the police used “brutally violent tactics” against the protesters, and called for the dismissal of Commissioner Shea and a policy change that would require the police to be more accountable to civilian review.

Mr. Stringer, Mr. Donovan and Mr. McGuire focused on what they saw as a failure of leadership.

“When I’m mayor, I’ll make certain that my police commissioner understands my values and the perspective of people who look like me,” said Mr. McGuire, who is Black.

Mr. Stringer, who has collected a string of endorsements from progressive candidates, called for “wholesale reform” because the Police Department operated without “real accountability.”

Mr. Adams, a former police officer, had perhaps the most moderate view among the major candidates. He said the report detailed “tactical errors and acts of heavy-handed policing” and called for more diverse leadership and enhanced de-escalation and implicit bias training.

Lawsuit against ranked-choice voting suffers setback

A lawsuit seeking to prevent the use of ranked-choice voting in the June primary was dealt a significant blow last week when a State Supreme Court judge declined to issue a temporary restraining order in the matter.

“This court is disinclined to take any action that may result in the disenfranchisement of even one voter or take any action that may result in even one voter’s ballot being nullified,” Justice Carol R. Edmead of State Supreme Court in Manhattan wrote in her ruling.

Under a new system approved by referendum last year, voters in primary and special elections can rank up to five candidates in order of preference. If no candidate receives a majority, the last-place winner is eliminated and the second-choice votes of those ballots are counted. The process continues until a candidate has won a majority.

But several members of the Black, Latino and Asian Caucus of the City Council have filed a lawsuit suggesting that voters had not been educated about the new process, and that people of color and immigrants would be disenfranchised as a result.

Two Black mayoral candidates, Mr. Adams, the borough president of Brooklyn, and Mr. McGuire, a businessman, both expressed concerns about Black voter disenfranchisement. Other Black mayoral candidates, Ms. Morales, a former nonprofit executive who is Afro-Latina, and Ms. Wiley, support the use of ranked-choice voting.

The ruling directly affects a Feb. 2 special election for a City Council seat in Queens, which is slated to be the city’s first contest to use ranked-choice voting since the referendum was passed. Justice Edmead noted that overseas ballots for the race were about to be mailed out.