Police matters dominated public comment at Monday’s lengthy meeting of the City Council, with several speakers urging a leader be appointed to the Police Review and Advisory Board to address issues surrounding the arrest of Harvard professor Henry Louis Gates Jr., a Sept. 24 youth altercation outside the Frisoli Youth Center and the return of community policing.

There are 15 cases awaiting investigation by the board, noted speaker Richard Clarey, an attorney, including the July 16 arrest of Gates on charges of disturbing the peace. The arrest of the black professor by a white police officer on Gates’ property made national headlines and led to a peace-making meeting with President Barack Obama.

“The city manager is obstructing the board,” Clarey said, referring to the city’ longtime chief executive, Robert W. Healy. “For the past 10 months, the board has not been able to function.” Critics say there is also a missing member, believe board investigator Joe Johnson is unable to address issues and worry Nancy Schlacter, acting executive director of the Cambridge Human Rights Commission, has been prevented from working with the panel, although she is qualified to do so.

In the youth center incident, about 20 youths outside were exchanging insults and racial epithets and beginning to push and shove each other when police were called; witnesses said it took police too long to respond. “I’ve never seen such violence. I was petrified,” said area resident Claire Koen, another speaker during Monday’s public comment with concerns including trash collection and a growing number of rats.

Koen, her voice trembling, asked, “What happened to my city?”

Speakers including Clarey and council candidates Lawrence J. Adkins and Charles Marquardt suggested they know what happened: a loss of community policing in which officers walk or bicycle through neighborhoods, meeting residents before there is trouble, rather than showing up solely in response to an emergency call.

It was a mistake moving police headquarters to Sixth Street in Kendall Square, away from the Green Street headquarters in Central Square, they said. The 25-person Central Square drug bust Sept. 10-12 shouldn’t have been necessary, Clarey said. “When the police were in Central Square, [that situation] wouldn’t exist,” he said.

And Adkins worried that in times of high unemployment, with many younger people out late to visit friends, police are stopping pedestrians unfairly, even based solely on race. It wouldn’t be a concern with a return to community policing, he said.

“They need to get out of that mindset that they can be out of the city, on the outskirts,” he said of police. “We had police officers on foot and bicycle in my neighborhood.  That no longer exists.”

Stopped outside the Sullivan Chambers in City Hall, Healy interrupted a reporter’s question to say he didn’t have time to get into police issues.

The council also heard comments and questions on money spent to keep public pools open; on traffic safety on the Alewife Brook Parkway near Mount Auburn Hospital; and on several homeowners’ years-long wish to leave the Avon Hill Neighborhood Conservation District, claiming its construction rules are unfairly strict.

Public comment was just the beginning of a prolonged, election-season meeting, with questions and answers even on relative minutiae — how long it takes to cross a portion of Massachusetts Avenue between two crosswalks, responsibility for the cigarette butts that fall between bricks near sidewalk dining — slowing council and city manager business to a crawl.

The council started by discussing the pools at length, with proposals being floated for the city taking over the full expense, seeking sponsorship from a deep-pocketed company such as Microsoft Corp., which has offices in Cambridge — both allowing the pools to stay open later during the summer without reliance on the state budget —  and looking into new river-based pool structures. Healy resisted (giving a flat “no” that drew laughs) to taking on full responsibility for the pools, and City Councilor Marjorie C. Decker said, “The state is trying to dump this in our laps.” Councilors and Healy agreed funding talks with the city’s legislative delegation were in order.

The lack of lifeguards when student employees left for college had been given as one reason for closing pools. City Councilor David P. Maher called that “a bogus argument,” backed by City Councilor Kenneth E. Reeves.