Near the end of a long day of radio and TV appearances from home, Robert Kelly, an expert on East Asian affairs, prepared for another live video interview at 7 p.m.

As he finished up a soda and tightened his necktie before a Skype call from the BBC, he forgot to lock the door of his office in his high-rise apartment in Busan, South Korea’s second-biggest city, something he usually does.

That oversight has set off one of the biggest viral internet sensations of the year, featuring cameo appearances in the Friday interview by his wife and two young children. The buzz has even overshadowed the major news Mr. Kelly was on air to discuss: the impeachment of South Korea’s president.

“It’s a comedy of errors,” Mr. Kelly said in an interview with The Wall Street Journal.

As Mr. Kelly began his BBC appearance, his wife, Kim Jung-A, was with their two children in the living room, watching it. To ensure he had a copy of the clip, Ms. Kim videoed the TV screen with her phone.