If there was mobs and bosses in your home, perhaps you could buy NPC's from the crown shop to give out quests. The NPC's would only be able to give out certain quests, or you would have to buy the quests from the crown shop (or you would pay crowns to customize a quest). You would only be able to have 3 quests in your home and you would only be able to complete 1 house-quest every day, even if it wasn't from your house. Only 1 of your houses would be able to support quests.
To customize a quest, you would place your NPC, then hover your mouse over it. Like adding words to a sign, a button would show up. It would say something similar to 'Add quest'. An NPC should only be able to give out 2 quests, and if you want to have a quest line between 2-3 NPCs then it could be 4-5 objectives long. However, if you choose to have a line of quests, you wouldn't be able to have 2 quest lines.
I'm thinking the quest customizer would be a similar format to naming your wizard. You would move the arrows up and down; the first arrow could be selecting whether you will collect or defeat something. Then, you will select what to collect or defeat; if you have not placed mobs/bosses or things to collect in your home, you cannot make a quest. After that is done, you may select the prize. The prize should be limited to useless clothing, gold, and experience.
Now we are presented with another problem; who will voice the dialogue of these NPCs? Well, the answer is simple. No one. You could simply play a sound clip similar to adults talking in Charlie Brown movies until they're done talking. Otherwise, you would just read it.
The last and biggest issue is putting this into the game. No one knows if it'll be able to handle it, but, we HAVE put fishing in houses AND we have 9 worlds to quest through. If this idea seems a bit far-fetched to you, Kingsisle, I'm fine with that. However, if you did add this to the game in some way, I can gurantee that it would make the game much more interesting.