Dustin Jones must navigate an obstacle course every time he goes out.

Mr. Jones, who uses a wheelchair, gets stuck at sidewalk corners where the curb ramp is too broken to roll over or missing altogether. He has to keep going around the block until he finds a usable ramp. The one time he tried to roll off a curb without a ramp, he almost tipped over into the street. He never did that again.

“I’m not able to move around like I want to on the sidewalk like every other New Yorker,” said Mr. Jones, 29, a disability rights advocate who lives in the Bronx. “I believe it’s very unfair. These types of things should not be happening in a city like this.”

Mr. Jones is part of a long-running battle over New York City’s 162,000 sidewalk corners that has resulted in more than two decades of litigation. In the latest development, a federal court-ordered report has highlighted numerous shortcomings in the city’s efforts to install and maintain curb ramps to make every corner accessible to people with disabilities.

The report, by Robert L. Burgdorf Jr., an expert on disability rights, was issued as part of a federal lawsuit filed by the Eastern Paralyzed Veterans Association, now known as the United Spinal Association, against the city in 1994. In spite of a subsequent 2002 settlement, and another agreement last year to address continuing concerns, the report found that the majority of the city’s curb ramps are still not in compliance with federal requirements under the Americans with Disabilities Act, and that the city lacks even a comprehensive survey of all its corners or an adequate plan of action.