Both parties had teams at polling stations to spot potential problems
Isolated voting problems, long queues and electoral hoaxes were reported as Americans cast their ballots - but there were no serious hold-ups.
Some difficulties surfaced early on Tuesday as people turned out even before voting began in eastern states.
There were reports of glitches with electronic voting machines in states including Florida, Ohio and Virginia.
But most were minor malfunctions thought highly unlikely to affect the election's outcome.
Americans are especially watchful for problems with the vote after controversies in the last two elections.
Results of the 2000 poll were held up until the US Supreme Court decided to halt a recount over contested votes in Florida, leaving George W Bush the winner.
In Ohio, there was turmoil in 2004 over malfunctioning machines and long queues.
The 2008 contest was remarkable for the sheer number of voters that turned out at some 7,000 election jurisdictions across the US.
Millions of people voted early. Overall voter registration numbers were up 7.3% on 2004.
Turnout rates as high as 80% were expected in Virginia and California, the country's most populous state.
Election observers reported tens of thousands of complaints as polling stations struggled to cope with the high volume of voters.
Marjorie Lindblom, at a New York-based call centre, said her office had received an equally high number of complaints.
"Certainly the system is not adequate to deal with the kinds of turnout we're having. There are lots of problems with machines breaking down," Ms Linblom said.
"New York is using machines that I think are about 50 years old... Many voters are not sure their votes are registering properly."
In Kansas City there were reports that the wrong electoral rolls had been delivered to some polling stations, leading to delays.
In New Jersey, voters had to use paper ballots because of problems with electronic voting machines in some precincts, the Associated Press said.
Voters in Richmond, Virginia, were forced to wait after the person holding the keys to a branch library which was doubling as a polling station overslept.
At other counties in the state, there were paper jams and intermittent problems with electronic voting machines.
Ohio, which experienced extreme problems in the last presidential race, had some jammed paper problems with machines in Franklin County.
"We're taking care of things like that," elections spokesman Ben Piscitelli told AP. "But there's nothing major or systemic."
There were reports of a number of hoax calls, e-mails and flyers had been distributed in various states, some designed to convince people that voting had been postponed.
At George Mason University in Virginia, someone apparently hacked into the e-mail system and generated a message telling students the vote had been postponed until Wednesday.
Voting advocacy group Common Cause reported problems in the town of Greeley, in northern Colorado. The group said Spanish-speaking voters could not understand polling materials which were printed only in English, and that there were not enough interpreters.
One of the most bizarre incidents occurred in St Paul, Minnesota.
A car hit a utility pole, knocking out power for more than an hour in two polling stations.
Ballots were kept secure until electricity was restored, when they were run through an electronic machine.
Unsurprisingly, both the Democratic and Republican Parties have signed up lawyers in readiness for any rancorous disputes over voter identity, voting machine malfunctions and close counts.