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]
(..) Is he all right? I'm fine. I love you, but I wasn't talking to you. I mean, he was lucky. The exposure was very mild, but this gas attacks the upper respiratory tract. You could get nosebleeds followed by extreme dizziness, especially after physical exertion. (..)2011 TvShow: Dexter Title: Talk to the Hand Season: 6 Episode 11