The Trump campaign would not discuss its vetting process for hiring people, and it was unclear if Mr. Trump knew about Mr. Bannon’s brush with the law.

“I don’t know what he was aware of with respect to a 20-year-old claim where the charges were dropped,” Kellyanne Conway, Mr. Trump’s new campaign manager, told ABC News on Friday.

Mr. Bannon, Mr. Manafort and Mr. Stepien are not the first of Mr. Trump’s hires to come with baggage. Mr. Manafort’s predecessor, Corey Lewandowski, also came with some warning signs. As a congressional aide, he was once arrested after he brought a gun to work. He also ended up distracting Mr. Trump’s campaign after he was charged with battery in April for allegedly grabbing the arm of a reporter. Those charges were later dropped.

Mr. Trump, who once tried to trademark the phrase “you’re fired,” which he popularized as star of “The Apprentice,” has shown a tendency to hire with his gut in other instances. During a news conference at the construction site of his Washington hotel in March, he plucked a woman from the audience and offered her a job with his company.

“She seemed like a good person to me,” Mr. Trump said after the event.

Other presidential campaigns have had thorough vetting processes when bringing on new staff members. A former aide to Mitt Romney, who asked to remain anonymous to discuss the inner workings of that campaign, said that the 2012 nominee did extensive background checks and that potential hires who had even D.W.I. convictions did not make the cut.

Some said that Mr. Trump’s penchant for giving second chances could be a good thing, as people who have had personal or career setbacks often work harder to make the most of such opportunities.