When potentially embarrassing information is disclosed about an individual without relation to a legitimate public concern it may give rise to a claim of invasion of privacy. For example, wrestler Hulk Hogan sued Gawker for publishing sex tapes.
The claim. The Reporter's Committee has summarized the elements of a private-facts invasion of privacy claim: (1) the information is so personal and intimate that its disclosure would offend a reasonable person, even if the information is true; (2) the information is not generally known to the public; (3) the information is not newsworthy; and (4) the disclosure of the information is widely communicated. You can find summaries of a few lawsuits at the Digital Media Law Project.
Limiting liability. Your interview subjects can safely disclose any facts about themselves, for example, "I used to shoplift." But you would want to avoid identifying others involved, for example, "I used to shoplift with my cousin, Mark." You're okay disclosing private facts about a dead person as the dead have no privacy. You may also defend against a claim by demonstrating that your podcast is not "widely communicated," that the information is newsworthy, or that the information is generally known (for example, it's a matter of public record). If your podcast has a corporate affiliation or you've indemnified the sponsors, you should take a conservative approach as injured parties tend to pursue defendants with deep pockets (Although sometimes the injured parties are bankrolled by equally deep pockets).