If approved in Federal District Court in Manhattan, the settlement with prosecutors is likely to result in the appointment of a monitor to address the authority’s failures in lead inspections as well as a broad range of maintenance issues relating to heating, mold, vermin and pests in the city’s 176,000 public housing apartments.

Mayor Bill de Blasio signed the agreement with federal prosecutors in June to provide more than $1 billion to the authority over the next four years. The authority has estimated the cost of its outstanding repairs at more than $32 billion.

The areas of possible noncompliance described on Wednesday include administrative requirements tied to overtime and procurement, tenant protections during the eviction process as well as those emerging out of settlements with federal prosecutors over lead and mold, Ms. Flatley said. The authority is reviewing its handling of those aspects of its operations, and others, including whether it meets requirements for operations in an emergency.

In a telephone interview, Mr. Brezenoff said that when it comes to emergency management plans there may be “technical aspects” that are not being followed.

“I wasn’t ready to sign off that we have them all in 100 percent shape,” he said of the emergency management plans, but he added that he did not believe the compliance issues posed a danger to residents. “Nycha has been the subject of so much scrutiny that I can’t afford to ignore any area of noncompliance.”

Mr. Brezenoff described the agency’s work now as “in process” though he said, so far, the most serious compliance issues remained around the issue of lead testing.

The scene at the board meeting, of a Nycha official reading a statement admitting to failures, mirrored one a year before, when for the first time the agency publicly acknowledged that it had been certifying that required lead inspections had been done, when in fact they had not.