Technical problems with decrepit machines had caused some votes to be counted more than once or not at all. A badly designed ballot confused thousands of people. And a poorly executed purge of registration rolls led to eligible voters being turned away at the polls.

“What we learned in that was how confusing the entire process was,” said Adam Goodman, a Republican consultant who advised Florida’s secretary of state at the time, Katherine Harris, during the recount. “That was something the public back then didn’t understand. It still doesn’t understand.”

Fallout from the recount contributed to the passage of the federal Help America Vote Act, which allocated billions of dollars for states to improve technology, ensure voter access and secure systems against fraud. In Florida, legislators rewrote state laws, switched to paper ballots and optical scanners (no more butterfly ballots or hanging chads), and mandated automatic recounts for races with margins of half a percentage point.

Charles Stewart III, a leading expert on election administration at the Massachusetts Institute of Technology, said complaints about this month’s elections in some parts of the country should not be seen as evidence of a failing system, or lack of progress since 2000.

“Elections are incredibly complicated,” Mr. Stewart said, and officials are legally required to take time beyond Election Day to count votes. “Just the fact that we have a recount in Florida is leading people to say, ‘Ah, here we go again,’” he said. “In fact, it’s just a close election.”

Though it wasn’t a 2000 redux, the 2018 midterms exposed persistent problems and the haphazard way the voting process was administered across the country. In Arkansas, three-member boards handle elections at the county level, while in Connecticut all 169 towns and cities use their own registrars.

The inherently political nature of running elections can call into question some officials’ decision-making. In New York, party leaders fill county election boards in what critics say is little more than a patronage system.