Donald Trump, 77, has relentlessly attacked President Biden, 80, as too old for office. But the former president himself has had a series of gaffes that go beyond his usual freewheeling style.One of Donald J. Trump’s new comedic bits at his rallies features him impersonating the current commander in chief with an over-the-top caricature mocking President Biden’s age.With droopy eyelids and mouth agape, Mr. Trump stammers and mumbles. He squints. His arms flap. He shuffles his feet and wanders laggardly across the stage. A burst of laughter and applause erupts from the crowd as he feigns confusion by turning and pointing to invisible supporters, as if he does not realize his back is to them.But his recent campaign events have also featured less deliberate stumbles. Mr. Trump has had a string of unforced gaffes, garble and general disjointedness that go beyond his usual discursive nature, and that his Republican rivals are pointing to as signs of his declining performance.On Sunday in Sioux City, Iowa, Mr. Trump wrongly thanked supporters of Sioux Falls, a South Dakota town about 75 miles away, correcting himself only after being pulled aside onstage and informed of the error.It was strikingly similar to a fictional scene that Mr. Trump acted out earlier this month, pretending to be Mr. Biden mistaking Iowa for Idaho and needing an aide to straighten him out.In recent weeks, Mr. Trump has also told supporters not to vote, and claimed to have defeated President Barack Obama in an election. He has praised the collective intellect of an Iranian-backed militant group that has long been an enemy of both Israel and the United States, and repeatedly mispronounced the name of the armed group that rules Gaza.“This is a different Donald Trump than 2015 and ’16 — lost the zip on his fastball,” Gov. Ron DeSantis of Florida told reporters last week while campaigning in New Hampshire.“In 2016, he was freewheeling, he’s out there barnstorming the country,” Mr. DeSantis added. “Now, it’s just a different guy. And it’s sad to see.”It is unclear if Mr. Trump’s recent slips are connected to his age. He has long relied on an unorthodox speaking style that has served as one of his chief political assets, establishing him, improbably, among the most effective communicators in American politics.But as the 2024 race for the White House heats up, Mr. Trump’s increased verbal blunders threaten to undermine one of Republicans’ most potent avenues of attack, and the entire point of his onstage pantomime: the argument that Mr. Biden is too old to be president.Mr. Biden, a grandfather of seven, is 80. Mr. Trump, who has 10 grandchildren, is 77.Even though only a few years separate the two men in their golden years, voters view their vigor differently. Recent polls have found that roughly two out of three voters say Mr. Biden is too old to serve another four-year term, while only about half say the same about Mr. Trump.If that gap starts to narrow, it’s Mr. Trump who has far more to lose in a general-election matchup.Mr. Trump and President Biden are the front-runners for each party’s nomination, setting up the likelihood of a 2020 rematch. Michelle Gustafson for The New York TimesAccording to a previously unreported finding in an August survey from The Associated Press-NORC Center for Public Affairs Research, 43 percent of U.S. voters said both men were “too old to effectively serve another four-year term as president.” Among those voters, 61 percent said they planned to vote for Mr. Biden, compared with 13 percent who said the same about Mr. Trump.Last week, similar findings emerged in a Franklin & Marshall College poll of registered voters in Pennsylvania, one of the most closely watched 2024 battlegrounds.According to the poll, 43 percent of Pennsylvanians said both men were “too old to serve another term.” An analysis of that data for The New York Times showed that Mr. Biden led Mr. Trump among those voters by 66 percent to 11 percent. Among all voters in the state, the two men were in a statistical tie.Berwood Yost, the director of the Franklin & Marshall poll, said that Mr. Biden’s wide lead among voters who were worried about both candidates’ ages could be explained partly by the fact that Democrats are much more likely than Republicans to identify age as a problem for their party’s leader. “The age issue is one that if Trump gets tarred with the same brush as Biden, it really hurts him,” Mr. Yost said.Steven Cheung, a spokesman for the Trump campaign, noted that the former president maintained a commanding lead in Republican primary polls and that in the general election, several recent polls had shown Mr. Trump with slight leads over Mr. Biden.“None of these false narratives has changed the dynamics of the race at all — President Trump still dominates, because people know he’s the strongest candidate,” Mr. Cheung said. “The contrast is that Biden is falling onstage, mumbling his way through a speech, being confused on where to walk, and tripping on the steps of Air Force One. There’s no correcting that, and that will be seared into voter’s minds.”Mr. Trump’s rhetorical skills have long relied on a mix of brute force and a seemingly preternatural instinct for the imprecise. That beguiling combination — honed from a lifetime of real estate negotiations, New York tabloid backbiting and prime-time reality TV stardom — often means that voters hear what they want to hear from him.Mr. Trump’s speaking style has often meant that his supporters, or voters who are open to backing him, hear what they want to hear from him. Jordan Gale for The New York TimesTrump supporters leave his speeches energized. Undecided voters who are open to his message can find what they’re looking for in his pitch. Opponents are riled, and when they furiously accuse him of something they heard but that he didn’t quite precisely say, Mr. Trump turns the criticism into a data point that he’s unfairly persecuted — and the entire cycle begins anew.But Mr. Trump’s latest missteps aren’t easily classified as calculated vagueness.During a Sept. 15 speech in Washington, a moment after declaring Mr. Biden “cognitively impaired, in no condition to lead,” the former president warned that America was on the verge of World War II, which ended in 1945.In the same speech, he boasted about presidential polls showing him leading Mr. Obama, who is not, in fact, running for an illegal third term in office. He erroneously referred to Mr. Obama again during an anecdote about winning the 2016 presidential race.“We did it with Obama,” Mr. Trump said. “We won an election that everybody said couldn’t be won, we beat …” He paused for a beat as he seemed to realize his mistake. “Hillary Clinton.”At a Florida rally on Oct. 11, days after a brutal terrorist attack that killed hundreds of Israelis, Mr. Trump criticized the country for being unprepared, lashing out at its prime minister, Benjamin Netanyahu. Mr. Trump appears to have soured on Mr. Netanyahu, once a close ally, after the Israeli leader congratulated Mr. Biden for winning the 2020 election.In the same speech, Mr. Trump relied on an inaccurate timeline of events in the Middle East to criticize Mr. Biden’s handling of foreign affairs and, in the process, drew headlines for praising Hezbollah, the Iranian-backed militant group.Last week, while speaking to supporters at a rally in New Hampshire, Mr. Trump praised Viktor Orban, the strongman prime minister of Hungary, but referred to him as “the leader of Turkey,” a country hundreds of miles away. He quickly corrected himself.At another point in the same speech, Mr. Trump jumped into a confusing riff that ended with him telling supporters, “You don’t have to vote — don’t worry about voting,” adding, “We’ve got plenty of votes.”Mr. Cheung, the Trump campaign spokesman, said the former president was “clearly talking about election integrity and making sure only legal votes are counted.”Under Mr. Trump, the Republican Party has been dealt a series of electoral defeats since 2016. Doug Mills/The New York TimesIn a speech on Saturday, Mr. Trump sounded as if he were talking about hummus when he mispronounced Hamas (huh-maas), the Islamist group that governs the Gaza Strip and carried out one of the largest attacks on Israel in decades on Oct. 7.The former president’s pronunciation drew the attention of the Biden campaign, which posted the video clip on social media, noting that Mr. Trump sounded “confused.”But even Republican rivals have sensed an opening on the age issue against Mr. Trump, who has maintained an unshakable hold on the party despite a political record that would in years past have compelled conservatives to consider another standard-bearer. Mr. Trump lost control of Congress as president; was voted out of the White House; failed to help deliver a “red wave” of victories in the midterm elections last year; and, this year, drew 91 felony charges over four criminal cases.Nikki Haley, the 51-year-old former governor of South Carolina, opened her presidential bid this year by calling for candidates 75 or older to pass mental competency tests, a push she has renewed in recent weeks.On Saturday, Ms. Haley attacked Mr. Trump over his comments about Mr. Netanyahu and Hezbollah, suggesting in a speech to Jewish donors in Las Vegas that the former president did not have the faculties to return to the White House.“Let me remind you,” she added with a small smile. “With all due respect, I don’t get confused.”Jazmine Ulloa More