re: Nor not fessing up about an affair
No you don't get to lie to a grand jury with impunity. Usually a judge would use discretion in a case like this. Unless he was Republican, I guess.
Ask the framers what a high misdemeanor is. It must mean something more serious than:
1. A misdeed.
2. Law. An offense less serious than a felony.
Obvoiusly, they didn't intend presidents to be booted for spitting on the sidewalk, etc.