In historic Faneuil Hall, the mayoral race formally entered its final stretch at around 8 o’clock on Tuesday night when Mayor Thomas Menino and City Councillor At-Large Michael Flaherty stepped off the stage, having sparred during their final forum together.

Education dominated the 90-minute back-and-forth: Charging that the city was “stuck in neutral,” Flaherty continued to hit Menino over the city’s underperforming schools. Out of the city’s 143 schools, 100 of them have been labeled “underperforming” by the state, Flaherty pointed out in one of his stronger performances.

Menino said 75 percent of Boston schoolchildren go onto college and added the term “underperforming” was being used “liberally.” Under the state definition it means specific programs within the respective schools, and not the entire schools themselves, he said. “I’m proud of the progress we’ve made,” the mayor said. “Can we get better? Yes. we can.”

Many schools in Brookline, Weston, and Milton are rated underperforming as well, Menino added, prompting Flaherty to shoot back, “I’m not running for mayor of Brookline, Weston. …I’m running for mayor of Boston.”

Flaherty added: “Twenty-four thousand kids dropped out of Boston public schools [over 16 years]. Let’s ask ourselves: Are they working? Do they have an education? Are they in jail? Are they dead?”

Flaherty pledged that if there weren’t “significant” increases in graduation rates and enrollment after he is elected, he would not run for re-election. He also said that he has supported District 4 Councillor Charles Yancey’s unsuccessful efforts to bring a high school to Mattapan.

Menino pointed to rehabilitations of local schools, including the Jeremiah Burke High School on Washington St. The schools might be old, he said, but they can be fixed.

In a question from the audience about minority representation in his administration, Menino said he has three officials – or nearly a third of his cabinet – who are minorities: Carol Johnson, superintendent of schools, Larry Mayes, his human services chief, and Barbara Ferrer, who heads the Boston Public Health Commission.

“We have diversity,” Menino said, noting that he has lost two cabinet members of color in the last two years: housing chief Sandra Henriquez, who went to work for President Barack Obama, and former state Rep. Charlotte Golar Richie, who has worked for Gov. Deval Patrick. “I’m not going to stand here and say I’m perfect.”

Flaherty pointed to his teaming with City Councillor At-Large Sam Yoon, a Korean-American who lives in Fields Corner and came in third in the mayoral preliminary, as one example of the diversity that he will bring to his administration.

“It’s not just about window dressing,” Flaherty said. “It’s about respecting each and every one of you. You’ll all be part of the Flaherty administration.”

Asked if they would require random and mandatory alcohol and drug testing for public safety personnel, including firefighters, Flaherty, who has been endorsed by the firefighters union Local 718, said he would.

Menino said he also supported testing and has legislation pending on Beacon Hill mandating it. But he caught flak from Flaherty for not requiring it in previous union contracts he’s negotiated. “They want to get paid to take the test,” Menino said of the firefighters. “Is that fair? It’s not fair.”

The 90-minute forum was sponsored by MassVOTE, a nonpartisan voting rights group, and an array of local organizations and newspapers. Charles Ogletree, a Harvard Law School professor, moderated.