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]
(..) Ponton, go find security. Tell them I want to converse with Mr. Raymond Larocque. - You're not coming? - Something has come up. If the weather stays this mild, we are all in for a treat. - Place your bets. - I am in law enforcement too. Am I that obvious? No, it's just that I have an ear (..)1976 The Pink Panther Strikes Again
(..) Welcome to your new office. You should probably start by going through these files. It is lovely weather we are having. I hope the weather... ...stays this mild. If the weather continues... ...we are in for a lovely summer. The area is secure. - Are you all right? - Well, of course I'm all right. (..)1976 The Pink Panther Strikes Again