2- Behaving in a manner that is grossly incompatible with the office. The obvious example here is Bill Clinton.
You're already on the tricky one in point two. What's obvious for you might not be for others. Bill Clinton's cheating behavior was child's play compared to JFK's, to name one. But when the big dogs start barking the whole Land of Freedom barks. And when they don't, no Chihuahua does.
Coming to Tricky Baracky, do you really think that private sexual behavior is less compatible with the office than, say, keep on talking in an official occasion during the Queen's Anthem, being hushed by her in front of everyone and thus becoming the laughing stock of ... well, anyone who cares to notice? Trained waiters know better. Is there a minimum competence level which is compatible with "the office"? Does this level include the oratorical ability not to talk folly in case of teleprompter malfunction? We all know this guy isn't smarter than Bush II, but "we give a breathalyzer to asthmatic children in the ER", for fuck's sake!?.
But I truly admire the US ruling class artfulness in choosing a guy who's so hard to hate or even criticize for any fool around the world (Benghazi and Snowdengate under Romney, go figure ...).