The worst fears about a chaotic end to a chaotic campaign failed to materialize on Tuesday as the final day of voting went off with little more than sporadic glitches and confrontations even as the tension over the outcome and aftermath remained undiminished.The most litigated, disrupted and polarized election in generations came to a close with voters who had not already cast their ballots by mail or in person during early voting trooping to the polls on an Election Day redefined by the coronavirus pandemic.There were scattered problems and hints of battles still to be fought: The authorities in Michigan sought to hunt down the source of robocalls that warned voters to “stay home.” A federal judge ordered the Postal Service to make an intensive sweep for mail-in ballots that had yet to be delivered. And legal skirmishes broke out in and around Philadelphia as Republicans sought to challenge votes in the critical Democratic stronghold.With a record number of votes already having been cast, election officials across the country reported relatively smooth operations on Tuesday, with nothing more than the usual long lines at polling places — made longer by social distancing — and machine malfunctions.The scale of the turnout and the shift to mail voting led to slow counts in some major cities in battleground states. In Philadelphia, about 20 percent of the absentee ballots had been counted by 9 p.m. In Milwaukee, election officials said they would not be done until 5 a.m. on Wednesday at the earliest.Appearing after midnight in Wilmington, Del., Joseph R. Biden Jr., the Democratic nominee, called for patience as the count proceeded in the states where the outcome is likely to be determined, including Pennsylvania.“It ain’t over till every vote is counted, every ballot is counted,” Mr. Biden said.Early on Wednesday, President Trump said on Twitter, “We are up BIG,” and claimed without evidence that Democrats “are trying to steal the election,” an assertion that led Twitter to say his post was “disputed and may be misleading.”But while the process of determining the winner could well prove to be as contentious as Mr. Trump has threatened to make it, much of what experts had feared might happen on a most unusual Election Day did not come to pass.In the past several days and weeks, foreign countries interfered less than they had leading up to the 2018 midterm elections, the director of the National Security Agency, Gen. Paul M. Nakasone, told reporters on Tuesday. And although there were reports of Russian trolls trying to amplify debunked claims of election fraud, they were limited in scope and there was no evidence of either widespread hacking or rampant Election Day disinformation efforts.Fears of violence that led some shopkeepers and homeowners to board up their windows and doors had not been realized as of early Tuesday evening, and there were only scattered and limited reports of intimidation at voting precincts.By the end of a day that was expected to push the percentage of Americans voting to its highest level since 1908, with a predicted total of around 160 million votes, it had become clear that the nation’s creaky elections infrastructure was proving to be more resilient than either the Republicans or Democrats had expected.“We have not seen major systemic problems or attempts to obstruct voting,” said Kristen Clarke, president of the Lawyers’ Committee for Civil Rights Under Law, which runs the Election Protection Hotline, adding that problems had been “isolated and sporadic.”Conducted over weeks in which coronavirus infections reached new highs nationwide and with Mr. Trump aggressively seeking to cast doubt on the integrity of the voting system, the election posed challenges that both voters and the officials running it largely adapted to meet.Television images showed election workers in downtown Philadelphia making quick work of opening and counting stacks of mail ballots. Voters met long lines in Detroit with high spirits, and no major reports of unrest.Even in Georgia, which became a symbol for all of the challenges of the nation’s election infrastructure when its new voting system experienced a wholesale breakdown in the spring, officials reported generally “steady movement” at polling stations, despite reports of some nagging issues with malfunctioning voting machines.“It has been steady as she goes throughout the state,” Gabriel Sterling, an official at the Georgia secretary of state’s office, told a group of reporters in midafternoon on Tuesday. Waiting times around the state, he said, averaged two minutes.Across Omaha, lines at polling places were shorter than in past days. Lined up were people like Ann Roth, 57, a voter who said God told her that the president was going to win, and Happy Sadjo, 47, who immigrated from the West African nation of Togo and called Mr. Trump an “American dictator.”In polling locations across northern Philadelphia — a Democratic stronghold of the type that Mr. Biden is counting on to give him an edge in a vital battleground state — voters lined up as early as 6 a.m., an hour before the polls opened.“I think Philadelphia is ready for a change, and they’re going to turn out,” said Sonia Bacchus, who arrived at William Rowen Elementary School early and came equipped with a folding chair for the lines. “Oh yeah.”The vast expansion of early voting options could reveal a vastly different electorate: Of the 100 million voters who cast early ballots, nearly 30 percent did not vote in 2016, according to TargetSmart, a Democratic data firm.But arduous work lay ahead with the counting of the record volume of mail-in ballots, especially in states like Pennsylvania that do not start counting absentee ballots until Election Day and are likely to take days to complete the task.Democrats were keeping a particularly wary eye on the Postal Service, which reported that its processing system had not recorded the delivery to elections offices of some 300,000 ballots — and that mail slowdowns were particularly having adverse effects in Democratic party strongholds like Philadelphia, Detroit, Atlanta and South Florida.Judge Emmet G. Sullivan of the Federal District Court in Washington, D.C., ordered sweeps in trouble spots on Tuesday to ensure that all ballots are found and delivered. The Postal Service said it was working into the evening to try to meet the court’s demands, though on its own time frame.The entire voting process still faced the constant and continuing threat of litigation. Over the course of the election, more than 400 election-related lawsuits were filed across the country, and courts were still issuing major rulings as voting was getting underway. A federal appeals court in Texas rejected a Republican appeal to try and knock out more than 127,000 votes that had been cast at drive-through voting locations in Harris County.Updated Nov. 4, 2020, 4:02 a.m. ETOver the course of the day, Republicans accelerated their legal challenges in Pennsylvania, which both campaigns view as the likely epicenter of any legal fight over the ultimate result.As Republicans ratcheted up criticism of senior Democratic officials overseeing voting in the state, Republican candidates and activists filed suits in federal and state courts seeking to disqualify the votes of Pennsylvanians who were given an opportunity to fix problematic mail-in ballots that had already been received, or to file replacement, provisional ballots. Judges agreed to hear those cases on Wednesday.Election 2020 ›How to Follow the Election ResultsHere’s a guide to The Times’s election night coverage, no matter when, how or how often you want to consume it.If you just want results… There will be a results map on The Times’s home page, and yes, the infamous needle will be back — but only for Florida, Georgia and North Carolina, the only states providing granular enough information for our experts to make educated projections of uncounted votes.If you want constant updates… Times reporters are live-blogging all day and night. This will be your one-stop shop for minute-by-minute updates: race calls, on-the-ground reporting from swing states, news about any voting issues or disruptions, and more.If you want to check in every so often… Times journalists are also producing a live briefing from roughly 5 p.m. to 3 a.m. ET, with an overview of what’s happening in the presidential race, the Senate and House races, and the voting process itself.The Trump campaign also complained that election officials in Philadelphia were keeping the campaign’s observers too far from counting tables. The observers were there to observe the process as absentee ballots were processed and counted for potential challenges, but the campaign had yet to file suit as of late afternoon.In Nevada, the Trump campaign filed an emergency motion on Tuesday afternoon, asking the Nevada Supreme Court to halt the processing of some mail-in ballots in Clark County until local election officials allow for expanded access to observe the processing of mail ballots. The court denied the motion on Tuesday evening.Later, the Trump campaign successfully filed an emergency suit to extend poll hours in Clark County, which includes Las Vegas, by one hour.The efforts were part of Mr. Trump’s longstanding drive to raise doubts about the integrity of the entire voting system and give himself grounds to challenge any unfavorable outcome or lengthy counting process by claiming fraud.Though it threatened to undermine confidence in the final results, it also thrust voting rights to the center of the national political debate in a way not seen since the civil rights era, driving Democratic turnout, Biden campaign aides said.Election officials from both parties tended to agree, determining that all the questions about voting this year forced Americans to vote earlier, spreading the strain on the system across weeks and avoiding a single, last-minute crush.“Voters really thought about how they were going to vote months ago, and many had a plan and have executed on that,” said Kim Wyman, a Republican and the secretary of state in Washington, who oversees one of five predominantly vote-by-mail systems in the country and became an adviser to her colleagues in other states this year. “That’s exciting that we had that kind of engagement.”Still, the president’s attacks on the voting system also created an unusual situation in which his own supporters indicated to pollsters that they were less likely to vote by mail than their Democratic counterparts were, creating a bipartisan expectation that the president would lead the in-person, election-day vote and trail in the mail ballots.That divide on the degree of the threat from the pandemic was visible on Election Day. At a polling location in Dallas, an election judge refused to wear a mask inside, bringing complaints from voters throughout the day.At an afternoon news briefing with reporters during a visit to his Virginia campaign headquarters, the president renewed his complaint that the Supreme Court did not step in to block Pennsylvania’s decision to count all ballots with postmarks on or before Election Day that arrive at elections offices up to three days afterward.Several states are similarly planning to count late-arriving ballots, meaning that if the outcome is close, it may be days before the winner is known for sure.On Monday night, Twitter had flagged a post by Mr. Trump that predicted violence in response to the Supreme Court decision allowing Pennsylvania, for now, to stick to its extended counting deadline.And on Tuesday, it highlighted a statement by the Philadelphia District Attorney’s office debunking a claim amplified by Mr. Trump’s aides and supporters that Democrats had illegally hung a poster promoting the Biden ticket at a downtown polling station.“Misinformation being spread online has driven more calls to the Election Task Force hotline,” said Jane Roh, a spokeswoman for the Philadelphia district attorney, “than actual incidents at polling sites.”Nick Corasaniti reported from Philadelphia, Jim Rutenberg from New York and Stephanie Saul from Atlanta. Reporting was contributed by David E. Sanger, Julian E. Barnes and Luke Broadwater in Washington, and Dionne Searcy in Omaha.