• Mr. Kaine unleashed a blistering attack on Mr. Trump’s trail of contentious comments during the campaign, ticking off his remarks about Mexicans, women, African-Americans, an Indiana-born judge with Mexican heritage and Senator John McCain of Arizona. “I just want to talk about the tone that’s set from the top,” Mr. Kaine said. Mr. Pence said his running mate’s statements were “small potatoes” compared to Mrs. Clinton’s remark last month that half of Mr. Trump’s supporters fit into a “basket of deplorables.” Mr. Kaine replied that Mrs. Clinton had apologized for her remark — though, as Mr. Pence pointed out, her apology focused on the “half,” not the descriptor. Mr. Trump, Mr. Kaine said, has refused to apologize for any of his comments.

• Mr. Kaine condemned Mr. Trump’s foreign policy credentials, saying that the Republican nominee “can’t start a Twitter war with Miss Universe without shooting himself in the foot.” Mr. Pence suggested that Mr. Kaine sounded rehearsed. “Did you work on that one a long time?” he asked. Mr. Pence said that America was “less safe today” than it was when Mr. Obama took office.

• Sparring over refugee policies, Mr. Pence and Mr. Kaine fiercely defended their running mates’ approaches, with Mr. Pence arguing that Mrs. Clinton would expose the country to heightened risks. Mr. Kaine framed it another way: “We want to keep people out if they’re dangerous,” he said. “Donald Trump said, ‘keep them out if they’re Muslim.’”

• Mr. Pence, seizing on recent comments from Bill Clinton that appeared to be critical of the Affordable Care Act, said that “even former President Bill Clinton calls Obamacare a crazy plan.” (Mrs. Clinton’s team has moved this week to clarify his remarks, with her husband saying that he always supported the measure and still does.) Mr. Kaine did not immediately respond to the remark, setting off on an answer about Mrs. Clinton’s own economic plans.

• After Mr. Kaine mentioned Mr. Trump’s frequent praise of Vladimir Putin and the Trump campaign’s “shadowy connections with pro-Putin forces,” Mr. Pence blamed the Obama administration’s “weak and feckless foreign policy” for Russian aggression. “There’s an old proverb,” Mr. Pence said, “that says the Russian bear never dies, it just hibernates.”

• Mr. Kaine, turning repeatedly to Mr. Trump’s tax avoidance, sought to frame the issue as a matter of national security importance. After the attacks of Sept. 11, 2001, Mr. Kaine said, “young men and women signed up to serve in the military to fight terrorism” and Mrs. Clinton fought for constituents as a New York senator. “Donald Trump was fighting a very different fight,” he said: skirting tax payments that might have boosted American defenses.