He is, 'to put it mildly', a demanding boss. [=he is a very demanding boss]
He's 'mildly' [='slightly, somewhat'] interested in politics.
She was upset, 'to put it mildly'. [=she was extremely upset]
(..) - A little suffering's good for the soul. Hi, how are you? - My mouth is itchy. Is that normal? - Well, those symptoms won't last long. - I'm going to give you a mild sedative. - Oh, I wish I didn't know you. Don't be such an infant. How long is it supposed to... Unbelievable. (..)2009 Star Trek