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Watchdog groups reported complaints from people turned away from polls because they did not have identification in states like Pennsylvania, where ID was not required.
In swing states Virginia and Florida, long lines led to numerous complaints and fears that people would give up without casting a ballot, while large numbers of people in Ohio reported being forced to vote by provisional ballot.
It was unclear what impact the voting irregularities might have on an election that caps a close presidential campaign between Democratic President Barack Obama and Republican challenger Mitt Romney.
Throughout the day, voters in Pennsylvania, which saw court battles over controversial voter ID requirements, reported getting conflicting messages over whether an identification was required to vote.
A federal judge had ruled the new voter ID law could not be implemented this election because there was not enough time to ensure all registered voters had proper identification.
But poll workers were still requesting voter IDs, and reports surfaced of people being turned away if they could not produce one, witnesses and watchdog groups reported.
"Poll workers have been poorly and wrongfully trained, and they are standing there and sitting there and requiring people to show ID, and sending people home if they don't have the ID," said Barbara Arnwine, executive director of the Lawyers' Committee for Civil Rights.
The Lawyers' Committee, which helps run an Election Protection hot line that collects reports of problems at the polls, said there were signs outside some voting areas in parts of Pennsylvania falsely telling people they needed an ID.
Pennsylvania's ID rules were among a raft of new voting laws passed mostly by Republican-led legislatures in dozens of states since 2011. The courts have thrown out the harshest of the new laws, or at least ordered delayed implementation.
Republicans had their own complaints in Pennsylvania. The party got a court order to reinstate 75 Republican election officials in Philadelphia who allegedly were prohibited from entering polling places.
Election Protection had received more than 80,000 calls from people reporting various problems. Many of the calls came from Pennsylvania, New Jersey and New York.
In Ohio, many people complained they had been forced to vote by provisional ballot after their names did not appear on voter rolls.
Ohio regularly has the highest number of provisional ballots each presidential election, according to the Brennan Center for Justice at New York University's Law School. This year, numbers are likely to exceed 200,000 provision ballots, which will not be counted until at least November 17.
LINES SNAKE AROUND THE BLOCK
Long lines at polls in many states prompted concerns that some voters would walk away without casting ballots. Lengthy waits to vote were reported in Florida, Virginia and Ohio, all key swing states, as well as New Jersey and New York, states walloped a week ago by superstorm Sandy.
Virginia's State Board of Elections sent out a tweet urging voters waiting in line before the polls closed to stay to vote.
"If you were in line at 7pm and are eligible to vote, you will be able to cast a ballot, regardless of how long it takes!" the board said in the tweet.
In a sign of the importance of the Florida vote, Obama tweeted: "Reminder: If you're waiting to vote in Florida, #StayInLine! As long as you were in line when polls closed, you can still vote."
Voters reported hours-long lines throughout the day in Florida, where the Republican administration cut the number of early voting days to eight from 14.
About 12,000 voters in the Clearwater area of Florida received automated telephone calls on today telling them they had until the end of "tomorrow" to vote.
Once officials realised the problem, they called voters to tell them the message had been sent out a day late and the election was really today.
College students voting away from home also ran into problems in Florida after the new election law for the first time prohibited making address changes on the spot.
"Right now, it's annoying me," said Kristen Wiley, 20, a student from Boca Raton who said she had requested, but not received, an absentee ballot from Palm Beach County. She was waiting in line for a provisional ballot, knowing it would not count unless her eligibility is later verified.
Multiple problems were reported in New Jersey and New York, where Sandy crashed ashore eight days ago.
"There's just one word to describe the experience in New Jersey, and that is a catastrophe," Arnwine told reporters.
She said that computer servers had crashed, voters were being asked for ID that was not required, some polling places opened late and multiple locations did not have ballots.