A complaint prompted the inspection last week.
"We walk a fine line when it comes to enforcement," Harmon said. "We don't want to barge into people's homes, and they don't want us barging in."
Harmon said most of the city's landlords are responsible, and the quality of the housing stock has been upgraded over the past few years.
"I've seen a lot worse than this in my 20 years here," he said.
He said the Building Commission doesn't have "on the radar" any structures as bad as the one at 1411 Jackson St.
Most of the city's poorly kept homes are on the West Side and East End, Harmon said.
"We have more problems on the West Side than we do on the East End," he said. "But we have little patches of places that have issues all over the city."
The Rev. James Ealy, a Democratic councilman who represents a flat section of the West Side, agreed with Harmon that there were some problem homes and apartments in his ward. However, like Ealy and Sheets, he sees improvement.
"Things are getting a lot better, but it's still a problem," he said.
The high number of rental units and aging buildings contributes to the problem, Harmon said. Ealy believes another issue is landlords unwilling to spend money on repairs.
"The real bad guys are only concerned about making a dollar," Ealy said. "But I don't think there are that many of them anymore."
Like Sheets, Ealy tries to keep on eye on properties around his ward.
"We try to deal with the issues as we see them," he said.
Ealy first tries to talk to the landlords themselves to encourage them to clean up their property, he said. If that fails, he calls the building inspector.
Both Ealy and Sheets believe the approximately 2 1/2-year-old rental property registration requirement will help the city clean up problem properties.
"I think it has made a difference in this area," Ealy said.
Mayor Danny Jones said the law would help officials stay abreast of problems.
"We'll still have bad landlords, and we'll still have marginal landlords," Jones said. "But we'll have to stay on them."
Stone's property had been entered into the property registration database, Harmon said. However, he had only six of the seven units on the property registered.