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]
(..) Phil, stop the car. I wanna get out. Pull over. Get off the sidewalk. I should've been a fuckin' cop. Look, I already told you. You came in here with a mild concussion, some bruised ribs. No big deal. Although none of you could articulate how it happened. Do you remember how (..)2009 The Hangover