Lately, Mr. Trump has been experiencing his own adventures in aging for all to see. Last week, he bragged about passing a cognitive test when he was president but mixed up the name of the doctor who’d administered it. He has confused Nancy Pelosi with Nikki Haley, and Mr. Biden with Barack Obama.

And so Democrats have their own set of video clips they’ve been consuming, too — seeing evidence of aging in Mr. Trump’s curious tangents about sharks and boats with electric batteries, or in the way he bollixes up words, as he did at the rally Tuesday, when he barked at the Biden campaign for saying that “the videos of crooked Joe shuffling are clean fakes.” He asked the crowd, “Do you know what a clean fake is?” The term Mr. Trump was reaching for is actually “cheap fake” — real footage that has been edited deceptively, omitting context by zooming in or cropping out.

In Racine, some of Mr. Trump’s supporters took a more nuanced view of the videos of Mr. Biden, the age factor and how it all played into expectations for the debate.

“Oh, absolutely, we see them on every channel, and all over the internet of course,” Marjean Stern, 79, a retiree from Kenosha, Wis., said of the videos of Mr. Biden. But, given her own age, she confessed to feeling a little queasy at the way her candidate has reveled in Mr. Biden’s seemingly senior moments.

“We’re elderly, so we don’t like that,” she said. “I don’t want to make fun of him. I are him.”

Will Moes, 23, who just graduated from the University of Wisconsin-Madison and will be voting for the first time in a presidential election, said he accepted that videos of Mr. Biden might be edited to make him look addled. “But a lot of the context you see them in, when you watch the full videos, it’s hard to fake that,” he said.