The complexity of the cases should become greater as we go, I think. So starting with something as you said, a lost pet perhaps, seems reasonable. And yeah, I can certainly imagine Moriarty wanting to see just how capable Holmes is. I feel for every bit as confident as one is, so too is the other, so it'll inevitably turn into a sort of pissing contest to see who can best who. 

I also think it would be interesting if Irene were to begin to question her involvement down the road, actually turn to helping Holmes and company. It'd be discreet as she'd try to avoid tipping off Moriarty, so perhaps through things like dead drops or what have you. Regardless of what side she's on she won't be an obvious player, as I kind of think she has the mindset of waiting it out too, see who comes out on top so she can side with the victor.