There was the myth of Trump supporters sending wild dogs to scare off black voters in Ohio. In Texas, some of the voting booths supposedly became possessed, switching ballots cast for Donald J. Trump to Hillary Clinton. And then there was the amateur genealogist said to be committing voter fraud by jotting down names found on gravestones.

A week before Election Day, warnings of a rigged vote, amplified largely by Mr. Trump himself, have led to anxiety across the country about the integrity of the electoral process. In some instances, the concerns appear to be justified, but many have resulted from simple glitches or a heightened sense of suspicion. In any case, a year of extraordinary political polarization has left voters increasingly wary about their fellow citizens and the credibility of the country’s method for picking a president.

“I think there’s definitely more paranoia this year,” said Pamela Smith, the president of Verified Voting, a nonpartisan group that promotes the integrity of elections. “There has been a lot of talk about election rigging. If you think an election is going to be rigged, then you look at everything through that filter.”

Many of the rumors of rigged votes have taken on a life of their own on social media, where conspiracy theories flourish and accusations fly. The reports have left election officials and the local authorities scrambling to verify claims of mischief and, often, to offer reality checks.