How'd I guess that so early? Well, I'm a 58-year old reader who remembers a lot of what he's read (both fiction and non-fiction) and has enough imagination to see where things could apply.
I don't expect too much on-camera naughtiness from Harry & Hermione, but I wouldn't be surprised to see them occassionally turn up a bit "rumpled", sometimes unexpectedly. I suspect they'll find better places, but I could see them making a determined effort to evaluate every broom closet in Hogwarts - and then make the information generally available after they graduate. I can see that causing most "interesting" reactions among the staff. I could also see them doing this without getting caught due to their abilities.
A "vote of no confidence"? I wonder who'll be springing that on Albus, the Wizengamot or the Order? Either would be quite the "kick to the head' or "kick to the privates" (whichever would hurt Dumbles the most) and springing more on him would then add further insult to his injury (much like rubbing a heating rub on a highly bruised area). Viscious? Who, me?
58, huh? Well, you're only ten years older than me, and like you, I remember pretty much everything I read see or hear. It's not he wonderful gift most think it is.
Yes, they'll spend some 'quality time together and sometimes turn up a bit rumpled, but I'll let you guess where later.
The vote is for Fudge, not Dumbley, but I've arranged things for him too. Evil Chuckle!