Moist knew, even if nobody else did.
He'd been the one Billy-sorry, Dr. Horrible seemed to be his only name now-Dr. Horrible confided in about Penny (unless you counted all those video blog posts, but most people seemed to have forgotten about those).
He understood, even if the rest of this idiotic world didn't, that it had been Captain Hammer who he'd gone to the shelter to kill that night.
And Moist knew what it was doing to his boss.
He saw what was in his eyes during every heist, after every meeting with the League, whenever he thought he was alone in his lab, whenever he thought he was alone, period.
He knew, even when nobody else did, how completely and utterly broken Dr. Horrible was inside.
But what could he do about it?
It was his place to be the minion, especially now that they were finally in with the League and being kept busy all the time with pulling off evil schemes; this meant he was supposed to do what he could to help his boss, not be a therapist or confidant or whatever it was he needed. And Dr. Horrible barely talked to him now-I mean, yeah, he would give him orders and stuff, but not really talk to him. Sure, he could start the talking, but frankly, Moist wasn't sure any attempts to open a conversation about how his boss was feeling would be welcome.
So he did the only things he could do, which were obey orders, and make things damp.
And try not to show that he knew.
Hope this is in character; I know it's depressing, but the whole dang show is depressing because Joss Whedon hates happiness, so it probably fits.