A potentially messy fight over absentee ballots in Atlantic City, New Jersey, highlights Election Day concerns Tuesday about the possibility of fraudulent voting.

The Atlantic City mayoral race — which went to court Monday — turns on absentee ballots, which elections experts say is the easiest part of the voting system to exploit. In addition to organized fraud, however, some experts contend America’s failure to safeguard voter rolls creates the potential to influence the outcome of very close elections.

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This is especially true in two closely watched states, Virginia and New Jersey. The Public Interest Legal Foundation has uncovered thousands of noncitizens who have been illegally registered to vote, including hundreds who have cast ballots.

“Yes, noncitizens are going to vote in this election,” said Logan Churchwell, a spokesman for the election-integrity watchdog. “And some of them might do it in a completely innocent, naïve way.”

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The Atlantic City race pits incumbent Republican Don Guardian against City Councilman Frank Gilliam, the Democratic challenger. The Guardian campaign has objected to what it alleges is widespread fraud. On Monday, according to The Philadelphia Inquirer, New Jersey Superior Court Judge Julio Mendez ordered the Board of Elections to preserve all documentation associated with the mail ballots. But he denied a request by Guardian to be present when the board reviews the 6,100 mail-in ballots.

The newspaper reported that the election board met Monday evening to review ballots flagged by its staff. The Guardian campaign challenged 101 voters registered to a needle-exchange program, along with voters the campaign alleges were not properly registered to vote. In addition, the campaign contends voters named on a list 61 pages long received undisclosed assistance.

The Inquirer reported last week that Guardian hired two private detectives, who sent an informant with a recorder to volunteer for the Gilliam campaign, helping with an absentee ballot drive. The informant turned a requested absentee ballot in to a Democratic operative rather than taking it to the voter, and received a $30 fee.

The Gilliam campaign has accused Guardian of “desperation.”

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Churchwell said absentee voting is the weakest link in the voting system because many states have few safeguards to prevent fraud. He compared New Jersey law to Kansas. While Kansas requires voters to supply a driver’s license number in order to obtain an absentee ballot, New Jersey only requires the voter’s signature.

“We’ll have to see how that goes,” Churchwell said, referring to Guardian’s challenge. “The details are still very preliminary, and also quite partisan.”

Concerns over absentee ballot fraud also surfaced in Boston’s City Council race. Two community groups alleged that voters in the city’s Chinatown neighborhood were the victims of a “vote-farming” scheme.

The groups accused representatives of council candidate Mike Kelley of submitting more than 100 absentee ballot requests on behalf of elderly voters — many of whom do not speak English — and then gathered signatures on unsealed envelopes containing blank ballots. Kelley’s campaign denies any wrongdoing.

“Virginia’s response to our report is, ‘Hey, the system’s working.'”

The Public Interest Legal Foundation earlier this year found 5,556 noncitizens registered to vote in Virginia since 2011. The organization determined that 1,852 of those who were noncitizens had voted in past elections. In New Jersey, the group uncovered more than 1,000 noncitizens on the rolls. About a third of them had voted.

Churchwell acknowledged that these numbers are small compared to the total number of registered voters. They are more likely to sway close local elections and statewide contests with millions of voters. But he noted that Democrat Mark Herring defeated Republican Mark Obenshain by fewer than 1,000 votes out of almost 2.2 million cast in the 2013 Virginia attorney general’s race.

Given the state’s history with close races, Churchwell said, the reaction of Virginia officials to documented illegal voters is disturbing. He said officials have downplayed the issue by noting that the noncitizen voters have been removed from the rolls.

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“Virginia’s response to our report is, ‘Hey, the system’s working,'” he said.

But Churchwell said the illegal voters came to light only because they asked to be removed. He said it is impossible to know how many noncitizens might be registered — and voting — who have not voluntarily come forward.

Churchwell said the voting by noncitizens could trigger cancellation of their legal immigration status. That is why it is unconscionable for state officials to tolerate and even encourage noncitizens to register to vote, he said. That is true even if ballots cast by ineligible voters are unlikely to change the outcome of most elections.

“Tell that to them at their deportation hearing,” he said.