BIDEN'S CLAIM: Biden claimed that neither he nor the doctors he has spoken with had not seen a plan from the administration to distribute a COVID-19 vaccine. "There should be a plan," he said. "When we have the vaccine, how do we distribute it?"

FACT CHECK: The Trump administration does have a plan to distribute a potential COVID-19 vaccine, although the president has misrepresented how quickly it could be distributed.

Some of that plan was outlined in a Sept. 16 "Distribution Strategy," released jointly by the U.S. Department of Health and Human Services and Department of Defense.

The documents, according to HHS, provide an overview of distribution plans along with guidelines for "state, tribal, territorial, and local public health programs and their partners on how to plan and operationalize a vaccination response to COVID-19" in their communities.

The Trump administration also created "Operation Warp Speed," a partnership between HHS and DOD, as well as other private and federal agencies, to accelerate the research, development and eventual distribution of COVID-19 vaccines and treatments.

HHS Secretary Alex Azar has said that as part of Operation Warp Speed, federal officials have been laying the groundwork for vaccine delivery. "This in-depth, round-the-clock planning work with our state and local partners and trusted community organizations, especially through CDC, will ensure that Americans can receive a safe and effective vaccine in record time," Azar said in a press release last month.

Meanwhile, the Centers for Disease Control and Prevention executed a contract with McKesson -- the company that distributes the annual flu vaccine -- to distribute the COVID-19 vaccine when it becomes available.

Trump, though, has exaggerated how quickly most Americans could receive it, suggesting it would be widely available by the end of the year or even sooner. Federal public health officials and outside experts say most Americans will not be able to get vaccinated until well into next year.

-ABC News' Arielle Mitropoulos and Sony Salzman

In the last question of the town hall, Stephanopoulos asked Biden if he expects next week's debate to happen and if he would demand that Trump test negative. Biden said he expects to be at that debate and that he believes Trump will take a COVID-19 test.

He also mentioned that he had taken a COVID-19 test earlier Thursday.

"I just think it's -- it's just decency. To be able to determine whether or not you are -- you're clear," Biden said. "I'm less concerned about me than the people, the guys with the cameras, the people working in the, you know, the Secret Service guys you drive up with, all those people."

"I'm confident that the Cleveland Clinic is the one overseeing it," he added. "I think they're going to not let happen, what happened last time. They're going to demand that it's safe."

BIDEN'S CLAIM: "All the way back in the beginning of February, I argued that we should be keeping people in China. And we had set up, in our administration, a pandemic office within the White House."

FACT CHECK: Biden's comments about what his administration would have done differently at the beginning of the pandemic were lacking some context.

What Biden appeared to be referencing was the United States having Centers for Disease Control and Prevention staff based in China in order to monitor the spread of the virus. Reuters reported earlier this year that the Trump administration had cut the number of staff in China by more than two-thirds, mostly over the previous two years in the agency's Beijing office.

In a Democratic presidential primary debate in February, Biden referred to funding cuts for public health agencies. "What I would do immediately is restore the funding," he said then. "I would be on the phone with China and making it clear, we are going to need to be in your country."

His answer at the town hall Thursday night did not provide that full context, though, which made it sound like he could have been referring to whether he supported putting restrictions on travelers coming from China to the United States, a step President Donald Trump took at the beginning of February.

It was not until the beginning of April that Biden's campaign confirmed in a statement to CNN that he supported Trump's decision to bar some travel from China, because the move was supported by scientists and medical experts.

-ABC News' John Verhovek

Mieke Haeck, the mother of a transgender child, asked Biden how he would protect LGBTQ rights.

“I will flat-out just change the law. Eliminate those executive orders, number one,” Biden said.

Biden then brought up the high number of trans women of color who had been killed this year, and mentioned his late son Beau, who he said helped get the first transgender rights law passed in that state.

BIDEN'S CLAIM: “(If) my home was in a white neighborhood on one side of the highway and yours is in a Black neighborhood, same exact home, your home will start off being valued 29% less than my home, yet your insurance for that home will be higher. You'll be taxed more for it. We’ve got to end this.”

FACT CHECK: Biden’s statement is generally accurate.

After the town hall concluded, Biden’s campaign told ABC News he had been referring to a 2018 study by the Brookings Institution that found “homes of similar quality in neighborhoods with similar amenities are worth 23 percent less ($48,000 per home on average, amounting to $156 billion in cumulative losses) in majority black neighborhoods, compared to those with very few or no black residents.”

His campaign said Biden misspoke and meant to say 23%.

The 1968 Fair Housing Act is supposed to prevent discrimination that leads to those disparities. But civil rights groups and anti-poverty advocates have long argued that even with the law, cities and states can perpetuate housing segregation through zoning laws, insurance and lending policies, as well as tax credits that often favor wealthier white families over others.

Under Trump, Housing Secretary Ben Carson finalized a rule in August 2019 making it harder for people to allege discrimination – a proposal advocated by insurance companies and others in the housing industry that said regulations weren’t clear enough.

-ABC News' Anne Flaherty