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 (..)2006 The Pink Panther
(..) 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. (..)2006 The Pink Panther