In his weekly radio address, the mayor derided “an elections bureaucracy rife with patronage, mismanagement, incompetence, and waste,” called the Board of Elections “notoriously dysfunctional” and said it had a “dismal track record.” He urged residents who have trouble at the polls to call 311 for help.

“Inexplicable delays in reporting election results; misplaced and sometimes dramatically misreported returns; failures to open polling places on time or keep them operating efficiently: The sad litany of past Board of Elections bungles is a long one,” he said.

The problems last year — which occurred during an era when New York has claimed to be a capital of technology by welcoming outposts of Google and Facebook and planning a new technology campus on Roosevelt Island — were disheartening to advocates of easier voting.

Last year, it took 72 days to determine the winner of a special election for State Senate in Brooklyn, a process delayed by a recount and litigation. Weeks later, a hard-fought Congressional primary in Upper Manhattan and the Bronx was cast into doubt when the board released election night totals that did not include votes from some precincts. As recently as July, the board said it had discovered uncounted ballots cast in last year’s presidential election.

Government watchdog groups and civil rights organizations have a variety of concerns this year. They worry that the lever voting machines, stored under plastic covers in a pair of Brooklyn warehouses and largely forgotten for the past several years, might break down. They fret about the sizable number of poll workers who are familiar only with the optical scanners. And they fear rampant confusion among voters — on Sunday, the home page for the Board of Elections still featured the instructions, “Vote the New Way,” along with a large photograph of an electronic voting machine, and there was no sample ballot displayed.

“It’s really going to be very hard to predict what’s going to happen,” said Kate Doran, the election specialist for the League of Women Voters of the City of New York. “My own feeling is you’re going to have voters who have never voted on these levers before, you’re going to have poll workers who are poorly trained, and we’ll get machine breakdowns which will send us into a paper-ballot system. That’s the worst case.”