The case of Mark Zuckerberg becoming the next president candidate is one of the interesting cases that maybe wasn't difficult to predict, but what is more interesting is the cultural heritage that follows. By culture, I mean everything social connected to a person: customs, firm beliefs, the social environment - everything that the person has experience from, everything he or she has experienced and that we know will affect that person's decisions.
And speaking of social. Do you see the conflict of interest in that the candidate in theory has access to private information about roughly one billion people, information that these people have given voluntarily? Not counting the enterprises, but they are important contributors, too. This is not a scenario you want to have. In theory, this opens up for surveillance and unethical rule backwards - because it started well before the candidate was openly interested in a candidature.
This being utterly serious, though not limited by law, brings us to the next thought. What other types of background or connections are not desirable for presidents to have?