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]
(..) Sure. I have all his receipts. Your friend... Listen, whatever you say, I'm behind you per cent. ...he's an arrogant sod. Well, that was mild. People say a lot worse than that. This is what you wanted, isn't it? The journalist's diary? What kind of a boss was he, Amanda? Appreciative? (..)2010 TvShow: Sherlock Title: The Blind Banker Season: 1 Episode 2