Papa John's Pizza founder John Schnatter, comic Roseanne Barr, movie mogul Harvey Weinstein, chef Mario Batali, and before that, Uber's Travis Kalanick: the “hits” (to reputations) just keep on coming.

The list of big names and the enterprises linked to them that have foundered or worse because of flawed conduct—or allegations of it—goes on and on these days. Now it's CBS Corp.'s CEO Les Moonves facing accusations of past sexual misconduct. This week, NASCAR's CEO took an indefinite leave of absence after being arrested and charged with DUI and drug possession charges in New York.

The accelerant of social media is making it even harder to stamp out the flames of scandal than in the past, lawyers and crisis-management specialists say. Crises that used to take days to build in the news media ignite instantly thanks to Twitter, Instagram and Facebook. At the same time, it seems the number of corporate brands built around real-life personalities such as Batali or Schnatter are rising, presenting ever more possibilities for trouble.